Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/TRS/   (Beweissystem der NASA Version 6.0.9©)  Datei vom 28.9.2014 mit Größe 2 MB image not shown  

Quelle  critical_pairs.prf

  Sprache: Lisp
 

(critical_pairs
 (IMP_critical_pairs_aux_TCC1 0
  (IMP_critical_pairs_aux_TCC1-1 nil 3420229945
   ("" (lemma "var_countable") (("" (propax) nil nil)) nil)
   ((var_countable formula-decl nil critical_pairs nil)) nil))
 (CP?_TCC1 0
  (CP?_TCC1-1 nil 3395743409
   ("" (skosimp*)
    (("" (lemma "ext_preserv_pos")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (Sub? const-decl "bool" substitution nil)
    (V const-decl "set[term]" variables_term nil)
    (positions? type-eq-decl nil positions nil)
    (member const-decl "bool" sets nil) (set type-eq-decl nil sets nil)
    (lhs const-decl "term" rewrite_rules nil)
    (rewrite_rule type-eq-decl nil rewrite_rules nil)
    (rewrite_rule? const-decl "bool" rewrite_rules nil)
    (positionsOF def-decl "positions" positions nil)
    (positions type-eq-decl nil positions nil)
    (term type-decl nil term_adt nil)
    (position type-eq-decl nil positions nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil nat_types nil))
   nil))
 (CP_lemma_aux1a_TCC1 0
  (CP_lemma_aux1a_TCC1-1 nil 3406618276
   ("" (skosimp*)
    (("" (hide-all-but 2)
      (("" (typepred "alpha!1" "rho!1")
        (("" (hide -3) (("" (rewrite "subs_o"nil nil)) nil)) nil))
      nil))
    nil)
   ((subs_o formula-decl nil substitution nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (term type-decl nil term_adt nil) (set type-eq-decl nil sets nil)
    (V const-decl "set[term]" variables_term nil)
    (Sub? const-decl "bool" substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (Ren? const-decl "bool" substitution nil)
    (Ren type-eq-decl nil substitution nil))
   nil))
 (CP_lemma_aux1a 0
  (CP_lemma_aux1a-1 nil 3406746822
   ("" (skosimp*)
    (("" (lemma "exists_renaming")
      (("" (inst -1 "Vars(lhs(e2!1))" "Vars(lhs(e1!1))")
        (("1" (skosimp*)
          (("1" (lemma "inverse_renaming")
            (("1" (inst?)
              (("1" (skosimp*)
                (("1" (lemma "inverse_rename_identity")
                  (("1" (inst -1 "rho!1" "rho1!1" "lhs(e2!1)")
                    (("1" (prop)
                      (("1" (inst 2 "comp(sg2!1, rho1!1)" "rho!1")
                        (("1" (split)
                          (("1" (lemma "vars_term_rename")
                            (("1" (inst?)
                              (("1"
                                (assert)
                                (("1"
                                  (lemma
                                   "IUnion_extra[(V)].disjoint_subset")
                                  (("1"
                                    (inst
                                     -1
                                     "Vars(lhs(e1!1))"
                                     "Vars(lhs(e1!1))"
                                     "Vars(ext(rho!1)(lhs(e2!1)))"
                                     "restrict[term[variable, symbol, arity], ((V)), boolean](Ran(rho!1))")
                                    (("1"
                                      (assert)
                                      (("1"
                                        (hide-all-but 1)
                                        (("1"
                                          (expand"subset?" "member")
                                          (("1" (skeep) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide (-4 2))
                            (("2" (rewrite "o_ass")
                              (("2"
                                (rewrite "ext_o")
                                (("2"
                                  (expand "o")
                                  (("2" (replaces -1) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (rewrite "subs_o"nil nil))
                        nil)
                       ("2" (hide-all-but (-2 1))
                        (("2" (expand"subset?" "member")
                          (("2" (skosimp*)
                            (("2" (decompose-equality -2)
                              (("2"
                                (inst -1 "x!1")
                                (("2"
                                  (iff)
                                  (("2" (assertnil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (hide-all-but 1)
          (("2" (rewrite "vars_of_term_finite"nil nil)) nil)
         ("3" (hide-all-but 1)
          (("3" (rewrite "vars_of_term_finite"nil nil)) nil))
        nil))
      nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (exists_renaming formula-decl nil substitution nil)
    (vars_of_term_finite formula-decl nil subterm nil)
    (Ren type-eq-decl nil substitution nil)
    (Ren? const-decl "bool" substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (Sub? const-decl "bool" substitution nil)
    (inverse_rename_identity formula-decl nil substitution nil)
    (subs_o formula-decl nil substitution nil)
    (disjoint_subset formula-decl nil IUnion_extra nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (subset? const-decl "bool" sets nil)
    (ext def-decl "term" substitution nil)
    (restrict const-decl "R" restrict nil)
    (Ran const-decl "set[term]" substitution nil)
    (vars_term_rename formula-decl nil substitution nil)
    (o_ass formula-decl nil substitution nil)
    (O const-decl "T3" function_props nil)
    (ext_o formula-decl nil substitution nil)
    (rho1!1 skolem-const-decl "Ren[variable, symbol, arity]"
     critical_pairs nil)
    (sg2!1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs nil)
    (comp const-decl "term" substitution nil)
    (Dom const-decl "set[(V)]" substitution nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (inverse_renaming formula-decl nil substitution nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (e1!1 skolem-const-decl "{e1 | member(e1, E!1)}" critical_pairs
     nil)
    (term type-decl nil term_adt nil) (set type-eq-decl nil sets nil)
    (V const-decl "set[term]" variables_term nil)
    (is_finite const-decl "bool" finite_sets nil)
    (Vars const-decl "set[(V)]" subterm nil)
    (rewrite_rule? const-decl "bool" rewrite_rules nil)
    (rewrite_rule type-eq-decl nil rewrite_rules nil)
    (lhs const-decl "term" rewrite_rules nil)
    (member const-decl "bool" sets nil)
    (E!1 skolem-const-decl "set[rewrite_rule]" critical_pairs nil)
    (e2!1 skolem-const-decl "{e2 | member(e2, E!1)}" critical_pairs
     nil))
   shostak))
 (CP_lemma_aux1_TCC1 0
  (CP_lemma_aux1_TCC1-1 nil 3402063728
   ("" (skosimp*)
    (("" (hide-all-but (-1 2))
      (("" (rewrite "ext_preserv_pos"nil nil)) nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (Sub type-eq-decl nil substitution nil)
    (Sub? const-decl "bool" substitution nil)
    (V const-decl "set[term]" variables_term nil)
    (member const-decl "bool" sets nil) (set type-eq-decl nil sets nil)
    (lhs const-decl "term" rewrite_rules nil)
    (rewrite_rule type-eq-decl nil rewrite_rules nil)
    (rewrite_rule? const-decl "bool" rewrite_rules nil)
    (term type-decl nil term_adt nil)
    (position type-eq-decl nil positions nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil nat_types nil)
    (ext_preserv_pos formula-decl nil substitution nil))
   nil))
 (CP_lemma_aux1 0
  (CP_lemma_aux1-1 nil 3402063736
   ("" (skosimp*)
    (("" (lemma "CP_lemma_aux1a")
      (("" (inst?)
        (("" (assert)
          (("" (skosimp*)
            ((""
              (case "ext(union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))))(subtermOF(lhs(e1!1), p!1)) = ext(union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))))(ext(rho!1)(lhs(e2!1)))")
              (("1" (lemma "unification")
                (("1"
                  (inst -1 "subtermOF(lhs(e1!1), p!1)"
                   "ext(rho!1)(lhs(e2!1))")
                  (("1" (prop)
                    (("1" (skosimp*)
                      (("1" (copy -1)
                        (("1" (expand "mgu" -1)
                          (("1" (flatten)
                            (("1" (hide -1)
                              (("1"
                                (inst
                                 -1
                                 "union_subs(restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                (("1"
                                  (expand "member" -1)
                                  (("1"
                                    (expand "U" -1)
                                    (("1"
                                      (expand "unifier" -1)
                                      (("1"
                                        (assert)
                                        (("1"
                                          (expand "<=")
                                          (("1"
                                            (skosimp*)
                                            (("1"
                                              (inst
                                               2
                                               "ext(theta!1)(rhs(e1!1))"
                                               "replaceTerm(ext(theta!1)(lhs(e1!1)), ext(theta!1)(ext(rho!1)(rhs(e2!1))),p!1)"
                                               "tau!1")
                                              (("1"
                                                (lemma "ext_o")
                                                (("1"
                                                  (inst
                                                   -1
                                                   "tau!1"
                                                   "theta!1")
                                                  (("1"
                                                    (decompose-equality
                                                     -1)
                                                    (("1"
                                                      (split)
                                                      (("1"
                                                        (hide -1)
                                                        (("1"
                                                          (expand
                                                           "CP?")
                                                          (("1"
                                                            (inst
                                                             1
                                                             "theta!1"
                                                             "rho!1"
                                                             "e1!1"
                                                             "e2!1"
                                                             "p!1")
                                                            (("1"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (inst
                                                         -1
                                                         "rhs(e1!1)")
                                                        (("2"
                                                          (expand "o")
                                                          (("2"
                                                            (replace
                                                             -1
                                                             1
                                                             rl)
                                                            (("2"
                                                              (hide -1)
                                                              (("2"
                                                                (replace
                                                                 -1
                                                                 1
                                                                 rl)
                                                                (("2"
                                                                  (hide
                                                                   -1)
                                                                  (("2"
                                                                    (lemma
                                                                     "restriction_union")
                                                                    (("2"
                                                                      (inst
                                                                       -1
                                                                       "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                                                       "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                                                       "rhs(e1!1)")
                                                                      (("1"
                                                                        (lemma
                                                                         "dom_restriction")
                                                                        (("1"
                                                                          (copy
                                                                           -1)
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "Vars(lhs(e1!1))"
                                                                             "sg1!1")
                                                                            (("1"
                                                                              (inst
                                                                               -2
                                                                               "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                               "alpha!1")
                                                                              (("1"
                                                                                (lemma
                                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                                (("1"
                                                                                  (inst
                                                                                   -1
                                                                                   "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                   "Vars(lhs(e1!1))"
                                                                                   "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                   "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (prop)
                                                                                      (("1"
                                                                                        (replace
                                                                                         -1
                                                                                         1)
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "restriction_term")
                                                                                          (("1"
                                                                                            (inst?)
                                                                                            (("1"
                                                                                              (prop)
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (typepred
                                                                                                   "e1!1")
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "rewrite_rule?")
                                                                                                    (("2"
                                                                                                      (expand*
                                                                                                       "lhs"
                                                                                                       "rhs")
                                                                                                      (("2"
                                                                                                        (prop)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (hide-all-but
                                                                                         (-2
                                                                                          -3
                                                                                          -6
                                                                                          1))
                                                                                        (("2"
                                                                                          (lemma
                                                                                           "IUnion_extra[(V)].disjoint_subset")
                                                                                          (("2"
                                                                                            (inst
                                                                                             -1
                                                                                             "Vars(rhs(e1!1))"
                                                                                             "Vars(rhs(e1!1))"
                                                                                             "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                             "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                            (("2"
                                                                                              (prop)
                                                                                              (("1"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("1"
                                                                                                  (expand*
                                                                                                   "subset?"
                                                                                                   "member")
                                                                                                  (("1"
                                                                                                    (skeep)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 (-3
                                                                                                  1))
                                                                                                (("2"
                                                                                                  (lemma
                                                                                                   "IUnion_extra[(V)].disjoint_subset")
                                                                                                  (("2"
                                                                                                    (inst
                                                                                                     -1
                                                                                                     "Vars(rhs(e1!1))"
                                                                                                     "Vars(lhs(e1!1))"
                                                                                                     "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                                     "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                                    (("2"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (hide
                                                                                                         (-1
                                                                                                          2))
                                                                                                        (("1"
                                                                                                          (typepred
                                                                                                           "e1!1")
                                                                                                          (("1"
                                                                                                            (expand*
                                                                                                             "rewrite_rule?"
                                                                                                             "lhs"
                                                                                                             "rhs")
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide
                                                                                                         (-1
                                                                                                          2))
                                                                                                        (("2"
                                                                                                          (expand*
                                                                                                           "subset?"
                                                                                                           "member")
                                                                                                          (("2"
                                                                                                            (skeep)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (rewrite
                                                                         "restriction_Subs")
                                                                        nil
                                                                        nil)
                                                                       ("3"
                                                                        (rewrite
                                                                         "restriction_Subs")
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("3"
                                                        (lemma
                                                         "ext_replace_ext")
                                                        (("3"
                                                          (inst?)
                                                          (("3"
                                                            (prop)
                                                            (("1"
                                                              (replaces
                                                               -1)
                                                              (("1"
                                                                (copy
                                                                 -1)
                                                                (("1"
                                                                  (inst
                                                                   -1
                                                                   "ext(rho!1)(rhs(e2!1))")
                                                                  (("1"
                                                                    (inst
                                                                     -2
                                                                     "lhs(e1!1)")
                                                                    (("1"
                                                                      (expand
                                                                       "o")
                                                                      (("1"
                                                                        (replace
                                                                         -1
                                                                         1
                                                                         rl)
                                                                        (("1"
                                                                          (replace
                                                                           -2
                                                                           1
                                                                           rl)
                                                                          (("1"
                                                                            (replace
                                                                             -3
                                                                             1
                                                                             rl)
                                                                            (("1"
                                                                              (hide
                                                                               (-1
                                                                                -2
                                                                                -3))
                                                                              (("1"
                                                                                (lemma
                                                                                 "restriction_union")
                                                                                (("1"
                                                                                  (copy
                                                                                   -1)
                                                                                  (("1"
                                                                                    (inst
                                                                                     -1
                                                                                     "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                                                                     "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                                                                     "lhs(e1!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -2
                                                                                       "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                                                                       "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                                                                       "ext(rho!1)(rhs(e2!1))")
                                                                                      (("1"
                                                                                        (lemma
                                                                                         "dom_restriction")
                                                                                        (("1"
                                                                                          (copy
                                                                                           -1)
                                                                                          (("1"
                                                                                            (inst
                                                                                             -1
                                                                                             "Vars(lhs(e1!1))"
                                                                                             "sg1!1")
                                                                                            (("1"
                                                                                              (inst
                                                                                               -2
                                                                                               "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                               "alpha!1")
                                                                                              (("1"
                                                                                                (lemma
                                                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -1
                                                                                                   "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                   "Vars(lhs(e1!1))"
                                                                                                   "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                                   "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    (("1"
                                                                                                      (lemma
                                                                                                       "IUnion_extra[(V)].disjoint_commute")
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -1
                                                                                                         "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                         "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          (("1"
                                                                                                            (prop)
                                                                                                            (("1"
                                                                                                              (rewrite
                                                                                                               "union_commute")
                                                                                                              (("1"
                                                                                                                (replaces
                                                                                                                 -1)
                                                                                                                (("1"
                                                                                                                  (replaces
                                                                                                                   -1)
                                                                                                                  (("1"
                                                                                                                    (lemma
                                                                                                                     "restriction_term")
                                                                                                                    (("1"
                                                                                                                      (copy
                                                                                                                       -1)
                                                                                                                      (("1"
                                                                                                                        (inst
                                                                                                                         -1
                                                                                                                         "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                                                         "alpha!1"
                                                                                                                         "ext(rho!1)(rhs(e2!1))")
                                                                                                                        (("1"
                                                                                                                          (inst
                                                                                                                           -2
                                                                                                                           "Vars(lhs(e1!1))"
                                                                                                                           "sg1!1"
                                                                                                                           "lhs(e1!1)")
                                                                                                                          (("1"
                                                                                                                            (prop)
                                                                                                                            (("1"
                                                                                                                              (replace
                                                                                                                               -1
                                                                                                                               1
                                                                                                                               rl)
                                                                                                                              (("1"
                                                                                                                                (replace
                                                                                                                                 -2
                                                                                                                                 1
                                                                                                                                 rl)
                                                                                                                                (("1"
                                                                                                                                  (rewrite
                                                                                                                                   "ext_o")
                                                                                                                                  (("1"
                                                                                                                                    (expand
                                                                                                                                     "o")
                                                                                                                                    (("1"
                                                                                                                                      (case-replace
                                                                                                                                       "ext(alpha!1)(ext(rho!1)(rhs(e2!1))) = ext(sg2!1)(rhs(e2!1))")
                                                                                                                                      (("1"
                                                                                                                                        (hide-all-but
                                                                                                                                         (-10
                                                                                                                                          -12
                                                                                                                                          1))
                                                                                                                                        (("1"
                                                                                                                                          (replaces
                                                                                                                                           -1)
                                                                                                                                          (("1"
                                                                                                                                            (lemma
                                                                                                                                             "ext_o")
                                                                                                                                            (("1"
                                                                                                                                              (inst
                                                                                                                                               -1
                                                                                                                                               "alpha!1"
                                                                                                                                               "rho!1")
                                                                                                                                              (("1"
                                                                                                                                                (copy
                                                                                                                                                 -1)
                                                                                                                                                (("1"
                                                                                                                                                  (decompose-equality
                                                                                                                                                   -1)
                                                                                                                                                  (("1"
                                                                                                                                                    (decompose-equality
                                                                                                                                                     -2)
                                                                                                                                                    (("1"
                                                                                                                                                      (inst
                                                                                                                                                       -1
                                                                                                                                                       "lhs(e2!1)")
                                                                                                                                                      (("1"
                                                                                                                                                        (inst
                                                                                                                                                         -2
                                                                                                                                                         "rhs(e2!1)")
                                                                                                                                                        (("1"
                                                                                                                                                          (expand
                                                                                                                                                           "o")
                                                                                                                                                          (("1"
                                                                                                                                                            (replace
                                                                                                                                                             -1
                                                                                                                                                             *
                                                                                                                                                             rl)
                                                                                                                                                            (("1"
                                                                                                                                                              (replace
                                                                                                                                                               -2
                                                                                                                                                               *
                                                                                                                                                               rl)
                                                                                                                                                              (("1"
                                                                                                                                                                (hide
                                                                                                                                                                 (-1
                                                                                                                                                                  -2))
                                                                                                                                                                (("1"
                                                                                                                                                                  (lemma
                                                                                                                                                                   "same_substitution")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (inst
                                                                                                                                                                     -1
                                                                                                                                                                     "comp(alpha!1, rho!1)"
                                                                                                                                                                     "sg2!1"
                                                                                                                                                                     "lhs(e2!1)")
                                                                                                                                                                    (("1"
                                                                                                                                                                      (assert)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (lemma
                                                                                                                                                                         "same_term")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (inst
                                                                                                                                                                           -1
                                                                                                                                                                           "comp(alpha!1, rho!1)"
                                                                                                                                                                           "sg2!1"
                                                                                                                                                                           "rhs(e2!1)")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (prop)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (skosimp*)
                                                                                                                                                                              (("1"
                                                                                                                                                                                (hide
                                                                                                                                                                                 (-3
                                                                                                                                                                                  2))
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (inst
                                                                                                                                                                                   -2
                                                                                                                                                                                   "x!1")
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (assert)
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (hide
                                                                                                                                                                                       1)
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (typepred
                                                                                                                                                                                         "e2!1")
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (hide
                                                                                                                                                                                           -2)
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (expand
                                                                                                                                                                                             "rewrite_rule?")
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (flatten)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (expand*
                                                                                                                                                                                                 "subset?"
                                                                                                                                                                                                 "rhs"
                                                                                                                                                                                                 "lhs")
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (inst?)
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (assert)
                                                                                                                                                                                                    nil
                                                                                                                                                                                                    nil))
                                                                                                                                                                                                  nil))
                                                                                                                                                                                                nil))
                                                                                                                                                                                              nil))
                                                                                                                                                                                            nil))
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil)
                                                                                                                             ("2"
                                                                                                                              (hide-all-but
                                                                                                                               1)
                                                                                                                              (("2"
                                                                                                                                (expand*
                                                                                                                                 "subset?"
                                                                                                                                 "member")
                                                                                                                                (("2"
                                                                                                                                  (skeep)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil)
                                                                                                                             ("3"
                                                                                                                              (hide-all-but
                                                                                                                               1)
                                                                                                                              (("3"
                                                                                                                                (typepred
                                                                                                                                 "e2!1")
                                                                                                                                (("3"
                                                                                                                                  (expand
                                                                                                                                   "rewrite_rule?")
                                                                                                                                  (("3"
                                                                                                                                    (flatten)
                                                                                                                                    (("3"
                                                                                                                                      (lemma
                                                                                                                                       "rename_preserv_inclusion")
                                                                                                                                      (("3"
                                                                                                                                        (expand*
                                                                                                                                         "rhs"
                                                                                                                                         "lhs")
                                                                                                                                        (("3"
                                                                                                                                          (inst?)
                                                                                                                                          (("3"
                                                                                                                                            (assert)
                                                                                                                                            nil
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil)
                                                                                                                             ("4"
                                                                                                                              (hide-all-but
                                                                                                                               1)
                                                                                                                              (("4"
                                                                                                                                (expand*
                                                                                                                                 "subset?"
                                                                                                                                 "member")
                                                                                                                                (("4"
                                                                                                                                  (skeep)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (hide-all-but
                                                                                                               (-4
                                                                                                                -8
                                                                                                                1))
                                                                                                              (("2"
                                                                                                                (lemma
                                                                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                                                                (("2"
                                                                                                                  (case
                                                                                                                   "disjoint?(Vars(lhs(e1!1)), Vars(ext(rho!1)(rhs(e2!1))))")
                                                                                                                  (("1"
                                                                                                                    (inst
                                                                                                                     -2
                                                                                                                     "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                                     "Vars(lhs(e1!1))"
                                                                                                                     "Vars(ext(rho!1)(rhs(e2!1)))"
                                                                                                                     "Vars(ext(rho!1)(rhs(e2!1)))")
                                                                                                                    (("1"
                                                                                                                      (prop)
                                                                                                                      (("1"
                                                                                                                        (lemma
                                                                                                                         "IUnion_extra[(V)].disjoint_commute")
                                                                                                                        (("1"
                                                                                                                          (inst
                                                                                                                           -1
                                                                                                                           "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                                           "Vars(ext(rho!1)(rhs(e2!1)))")
                                                                                                                          (("1"
                                                                                                                            (assert)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil)
                                                                                                                       ("2"
                                                                                                                        (hide-all-but
                                                                                                                         1)
                                                                                                                        (("2"
                                                                                                                          (expand*
                                                                                                                           "subset?"
                                                                                                                           "member")
                                                                                                                          (("2"
                                                                                                                            (skeep)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (hide-all-but
                                                                                                                     (-1
                                                                                                                      -3
                                                                                                                      1))
                                                                                                                    (("2"
                                                                                                                      (typepred
                                                                                                                       "e2!1")
                                                                                                                      (("2"
                                                                                                                        (expand
                                                                                                                         "rewrite_rule?")
                                                                                                                        (("2"
                                                                                                                          (flatten)
                                                                                                                          (("2"
                                                                                                                            (expand*
                                                                                                                             "lhs"
                                                                                                                             "rhs")
                                                                                                                            (("2"
                                                                                                                              (lemma
                                                                                                                               "rename_preserv_inclusion")
                                                                                                                              (("2"
                                                                                                                                (inst
                                                                                                                                 -1
                                                                                                                                 "rho!1"
                                                                                                                                 "e2!1`1"
                                                                                                                                 "e2!1`2")
                                                                                                                                (("2"
                                                                                                                                  (assert)
                                                                                                                                  (("2"
                                                                                                                                    (inst
                                                                                                                                     -4
                                                                                                                                     "Vars(e1!1`1)"
                                                                                                                                     "Vars(e1!1`1)"
                                                                                                                                     "Vars(ext(rho!1)(e2!1`2))"
                                                                                                                                     "Vars(ext(rho!1)(e2!1`1))")
                                                                                                                                    (("2"
                                                                                                                                      (prop)
                                                                                                                                      (("2"
                                                                                                                                        (hide-all-but
                                                                                                                                         1)
                                                                                                                                        (("2"
                                                                                                                                          (expand*
                                                                                                                                           "subset?"
                                                                                                                                           "member")
                                                                                                                                          (("2"
                                                                                                                                            (skeep)
                                                                                                                                            nil
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("3"
                                                                                                              (hide-all-but
                                                                                                               (-5
                                                                                                                -8
                                                                                                                1))
                                                                                                              (("3"
                                                                                                                (lemma
                                                                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                                                                (("3"
                                                                                                                  (inst
                                                                                                                   -1
                                                                                                                   "Vars(lhs(e1!1))"
                                                                                                                   "Vars(lhs(e1!1))"
                                                                                                                   "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                                                   "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                                                  (("3"
                                                                                                                    (prop)
                                                                                                                    (("3"
                                                                                                                      (hide-all-but
                                                                                                                       1)
                                                                                                                      (("3"
                                                                                                                        (expand*
                                                                                                                         "subset?"
                                                                                                                         "member")
                                                                                                                        (("3"
                                                                                                                          (skeep)
                                                                                                                          nil
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("4"
                                                                                                              (hide-all-but
                                                                                                               (-3
                                                                                                                -7
                                                                                                                1))
                                                                                                              (("4"
                                                                                                                (lemma
                                                                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                                                                (("4"
                                                                                                                  (case
                                                                                                                   "disjoint?(Vars(ext(rho!1)(rhs(e2!1))), Vars(lhs(e1!1)))")
                                                                                                                  (("1"
                                                                                                                    (inst
                                                                                                                     -2
                                                                                                                     "Vars(ext(rho!1)(rhs(e2!1)))"
                                                                                                                     "Vars(ext(rho!1)(rhs(e2!1)))"
                                                                                                                     "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                                     "Vars(lhs(e1!1))")
                                                                                                                    (("1"
                                                                                                                      (prop)
                                                                                                                      (("1"
                                                                                                                        (hide-all-but
                                                                                                                         1)
                                                                                                                        (("1"
                                                                                                                          (expand*
                                                                                                                           "subset?"
                                                                                                                           "member")
                                                                                                                          (("1"
                                                                                                                            (skeep)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (hide
                                                                                                                     (-2
                                                                                                                      2))
                                                                                                                    (("2"
                                                                                                                      (typepred
                                                                                                                       "e2!1")
                                                                                                                      (("2"
                                                                                                                        (expand
                                                                                                                         "rewrite_rule?")
                                                                                                                        (("2"
                                                                                                                          (flatten)
                                                                                                                          (("2"
                                                                                                                            (lemma
                                                                                                                             "rename_preserv_inclusion")
                                                                                                                            (("2"
                                                                                                                              (inst
                                                                                                                               -1
                                                                                                                               "rho!1"
                                                                                                                               "e2!1`1"
                                                                                                                               "e2!1`2")
                                                                                                                              (("2"
                                                                                                                                (assert)
                                                                                                                                (("2"
                                                                                                                                  (inst
                                                                                                                                   -4
                                                                                                                                   "Vars(e1!1`1)"
                                                                                                                                   "Vars(e1!1`1)"
                                                                                                                                   "Vars(ext(rho!1)(e2!1`2))"
                                                                                                                                   "Vars(ext(rho!1)(e2!1`1))")
                                                                                                                                  (("2"
                                                                                                                                    (prop)
                                                                                                                                    (("1"
                                                                                                                                      (expand*
                                                                                                                                       "rhs"
                                                                                                                                       "lhs")
                                                                                                                                      (("1"
                                                                                                                                        (hide-all-but
                                                                                                                                         (-1
                                                                                                                                          2))
                                                                                                                                        (("1"
                                                                                                                                          (lemma
                                                                                                                                           "IUnion_extra[(V)].disjoint_commute")
                                                                                                                                          (("1"
                                                                                                                                            (inst
                                                                                                                                             -1
                                                                                                                                             "Vars(e1!1`1)"
                                                                                                                                             "Vars(ext(rho!1)(e2!1`2))")
                                                                                                                                            (("1"
                                                                                                                                              (assert)
                                                                                                                                              nil
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil)
                                                                                                                                     ("2"
                                                                                                                                      (hide-all-but
                                                                                                                                       1)
                                                                                                                                      (("2"
                                                                                                                                        (expand*
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                                                                                                                                         "member")
                                                                                                                                        (("2"
                                                                                                                                          (skeep)
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil)
                                                                                                                                     ("3"
                                                                                                                                      (expand*
                                                                                                                                       "rhs"
                                                                                                                                       "lhs")
                                                                                                                                      nil
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (hide-all-but
                                                                                         1)
                                                                                        (("2"
                                                                                          (rewrite
                                                                                           "restriction_Subs")
                                                                                          nil
                                                                                          nil))
                                                                                        nil)
                                                                                       ("3"
                                                                                        (hide-all-but
                                                                                         1)
                                                                                        (("3"
                                                                                          (rewrite
                                                                                           "restriction_Subs")
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("2"
                                                                                      (hide-all-but
                                                                                       1)
                                                                                      (("2"
                                                                                        (rewrite
                                                                                         "restriction_Subs")
                                                                                        nil
                                                                                        nil))
                                                                                      nil)
                                                                                     ("3"
                                                                                      (hide-all-but
                                                                                       1)
                                                                                      (("3"
                                                                                        (rewrite
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                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (hide-all-but
                                                               (-7 1))
                                                              (("2"
                                                                (rewrite
                                                                 "ext_preserv_pos")
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (hide-all-but (-6 1))
                                                (("2"
                                                  (rewrite
                                                   "ext_preserv_pos")
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (hide-all-but 1)
                                  (("2"
                                    (rewrite "restriction_Subs")
                                    nil
                                    nil))
                                  nil)
                                 ("3"
                                  (hide-all-but 1)
                                  (("3"
                                    (rewrite "restriction_Subs")
                                    nil
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide-all-but (-1 1))
                      (("2" (expand "unifiable")
                        (("2"
                          (inst 1
                           "union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))))")
                          (("1" (expand "unifier")
                            (("1" (propax) nil nil)) nil)
                           ("2" (hide-all-but 1)
                            (("2" (rewrite "restriction_Subs"nil
                              nil))
                            nil)
                           ("3" (hide-all-but 1)
                            (("3" (rewrite "restriction_Subs"nil
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (hide 3)
                (("2" (lemma "restriction_union")
                  (("2"
                    (inst -1 "restriction(sg1!1)(Vars(lhs(e1!1)))"
                     "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                     "subtermOF(lhs(e1!1), p!1)")
                    (("1" (lemma "dom_restriction")
                      (("1" (inst -1 "Vars(lhs(e1!1))" "sg1!1")
                        (("1"
                          (lemma "IUnion_extra[(V)].disjoint_subset")
                          (("1"
                            (inst -1
                             "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                             "Vars(lhs(e1!1))"
                             "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                             "Vars(ext(rho!1)(lhs(e2!1)))")
                            (("1" (lemma "dom_restriction")
                              (("1"
                                (inst
                                 -1
                                 "Vars(ext(rho!1)(lhs(e2!1)))"
                                 "alpha!1")
                                (("1"
                                  (assert)
                                  (("1"
                                    (lemma
                                     "IUnion_extra[(V)].disjoint_subset")
                                    (("1"
                                      (inst
                                       -1
                                       "Vars(lhs(e1!1))"
                                       "Vars(lhs(e1!1))"
                                       "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                       "Vars(ext(rho!1)(lhs(e2!1)))")
                                      (("1"
                                        (prop)
                                        (("1"
                                          (replaces -1)
                                          (("1"
                                            (lemma "restriction_union")
                                            (("1"
                                              (inst
                                               -1
                                               "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                               "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                               "ext(rho!1)(lhs(e2!1))")
                                              (("1"
                                                (lemma
                                                 "IUnion_extra[(V)].disjoint_commute")
                                                (("1"
                                                  (inst
                                                   -1
                                                   "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                   "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                                  (("1"
                                                    (assert)
                                                    (("1"
                                                      (lemma
                                                       "IUnion_extra[(V)].disjoint_subset")
                                                      (("1"
                                                        (inst
                                                         -1
                                                         "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                         "Vars(lhs(e1!1))"
                                                         "Vars(ext(rho!1)(lhs(e2!1)))"
                                                         "Vars(ext(rho!1)(lhs(e2!1)))")
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (prop)
                                                            (("1"
                                                              (rewrite
                                                               "union_commute")
                                                              (("1"
                                                                (replaces
                                                                 -1)
                                                                (("1"
                                                                  (lemma
                                                                   "restriction_term")
                                                                  (("1"
                                                                    (inst?)
                                                                    (("1"
                                                                      (prop)
                                                                      (("1"
                                                                        (replace
                                                                         -1
                                                                         1
                                                                         rl)
                                                                        (("1"
                                                                          (lemma
                                                                           "restriction_term")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                             "alpha!1"
                                                                             "ext(rho!1)(lhs(e2!1))")
                                                                            (("1"
                                                                              (prop)
                                                                              (("1"
                                                                                (replace
                                                                                 -1
                                                                                 1
                                                                                 rl)
                                                                                (("1"
                                                                                  (rewrite
                                                                                   "ext_o")
                                                                                  (("1"
                                                                                    (expand
                                                                                     "o")
                                                                                    (("1"
                                                                                      (propax)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil)
                                                                               ("2"
                                                                                (hide-all-but
                                                                                 1)
                                                                                (("2"
                                                                                  (expand*
                                                                                   "subset?"
                                                                                   "member")
                                                                                  (("2"
                                                                                    (skeep)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (hide-all-but
                                                                         1)
                                                                        (("2"
                                                                          (rewrite
                                                                           "vars_subterm")
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (hide-all-but
                                                               (-1 1))
                                                              (("2"
                                                                (rewrite
                                                                 "IUnion_extra[(V)].disjoint_commute")
                                                                nil
                                                                nil))
                                                              nil)
                                                             ("3"
                                                              (hide-all-but
                                                               1)
                                                              (("3"
                                                                (expand*
                                                                 "subset?"
                                                                 "member")
                                                                (("3"
                                                                  (skeep)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("4"
                                                              (hide-all-but
                                                               (-5
                                                                -6
                                                                1))
                                                              (("4"
                                                                (lemma
                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                (("4"
                                                                  (inst
                                                                   -1
                                                                   "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                   "Vars(lhs(e1!1))"
                                                                   "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                   "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                  (("4"
                                                                    (assert)
                                                                    (("4"
                                                                      (prop)
                                                                      (("1"
                                                                        (hide
                                                                         (-2
                                                                          -3))
                                                                        (("1"
                                                                          (lemma
                                                                           "IUnion_extra[(V)].disjoint_commute")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                             "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (hide
                                                                         (-1
                                                                          -2
                                                                          2))
                                                                        (("2"
                                                                          (expand*
                                                                           "subset?"
                                                                           "member")
                                                                          (("2"
                                                                            (skeep)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (hide-all-but 1)
                                                (("2"
                                                  (rewrite
                                                   "restriction_Subs")
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide-all-but (-1 1))
                                          (("2"
                                            (lemma "vars_subterm")
                                            (("2"
                                              (inst?)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (lemma
                                                   "IUnion_extra[(V)].disjoint_subset")
                                                  (("2"
                                                    (inst
                                                     -1
                                                     "Vars(subtermOF(lhs(e1!1), p!1))"
                                                     "Vars(lhs(e1!1))"
                                                     "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                     "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                                    (("2"
                                                      (prop)
                                                      (("2"
                                                        (hide-all-but
                                                         1)
                                                        (("2"
                                                          (expand*
                                                           "subset?"
                                                           "member")
                                                          (("2"
                                                            (skeep)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("3"
                                          (hide-all-but 1)
                                          (("3"
                                            (expand*
                                             "subset?"
                                             "member")
                                            (("3" (skeep) nil nil))
                                            nil))
                                          nil)
                                         ("4"
                                          (hide-all-but (-1 -4 1))
                                          (("4"
                                            (lemma
                                             "IUnion_extra[(V)].disjoint_subset")
                                            (("4"
                                              (inst
                                               -1
                                               "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                               "Vars(ext(rho!1)(lhs(e2!1)))"
                                               "Vars(lhs(e1!1))"
                                               "Vars(lhs(e1!1))")
                                              (("4"
                                                (lemma
                                                 "IUnion_extra[(V)].disjoint_commute")
                                                (("4"
                                                  (inst?)
                                                  (("4"
                                                    (assert)
                                                    (("4"
                                                      (prop)
                                                      (("1"
                                                        (hide
                                                         (-2 -3 -4))
                                                        (("1"
                                                          (lemma
                                                           "vars_subterm")
                                                          (("1"
                                                            (inst?)
                                                            (("1"
                                                              (assert)
                                                              (("1"
                                                                (lemma
                                                                 "IUnion_extra[(V)].disjoint_subset")
                                                                (("1"
                                                                  (inst
                                                                   -1
                                                                   "Vars(subtermOF(lhs(e1!1), p!1))"
                                                                   "Vars(lhs(e1!1))"
                                                                   "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                   "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                                                  (("1"
                                                                    (prop)
                                                                    (("1"
                                                                      (hide-all-but
                                                                       1)
                                                                      (("1"
                                                                        (expand*
                                                                         "subset?"
                                                                         "member")
                                                                        (("1"
                                                                          (skeep)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (hide
                                                                       (-1
                                                                        2))
                                                                      (("2"
                                                                        (lemma
                                                                         "IUnion_extra[(V)].disjoint_commute")
                                                                        (("2"
                                                                          (inst?)
                                                                          (("2"
                                                                            (assert)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (hide-all-but
                                                         1)
                                                        (("2"
                                                          (expand*
                                                           "subset?"
                                                           "member")
                                                          (("2"
                                                            (skeep)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide-all-but 1)
                      (("2" (rewrite "restriction_Subs"nil nil)) nil)
                     ("3" (hide-all-but 1)
                      (("3" (rewrite "restriction_Subs"nil nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("3" (hide-all-but 1)
                (("3" (rewrite "union_is_sub")
                  (("1" (hide 2)
                    (("1" (rewrite "restriction_Subs"nil nil)) nil)
                   ("2" (hide 2)
                    (("2" (rewrite "restriction_Subs"nil nil)) nil))
                  nil))
                nil)
               ("4" (hide-all-but (-1 1))
                (("4" (expand "disjoint_D?")
                  (("4" (lemma "dom_restriction")
                    (("4" (copy -1)
                      (("4" (inst -1 "Vars(lhs(e1!1))" "sg1!1")
                        (("4"
                          (inst -2 "Vars(ext(rho!1)(lhs(e2!1)))"
                           "alpha!1")
                          (("4"
                            (lemma "IUnion_extra[(V)].disjoint_subset")
                            (("4"
                              (inst -1
                               "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                               "Vars(lhs(e1!1))"
                               "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                               "Vars(ext(rho!1)(lhs(e2!1)))")
                              (("4" (assertnil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("5" (hide-all-but 1)
                (("5" (rewrite "restriction_Subs"nil nil)) nil)
               ("6" (hide-all-but 1)
                (("6" (rewrite "restriction_Subs"nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((CP_lemma_aux1a formula-decl nil critical_pairs nil)
    (subtermOF def-decl "term" subterm nil)
    (positions? type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions type-eq-decl nil positions nil)
    (Ren type-eq-decl nil substitution nil)
    (Ren? const-decl "bool" substitution nil)
    (lhs const-decl "term" rewrite_rules nil)
    (Vars const-decl "set[(V)]" subterm nil)
    (restriction const-decl "term" substitution nil)
    (union_subs const-decl "term" substitution nil)
    (disjoint_D type-eq-decl nil substitution nil)
    (disjoint_D? const-decl "bool" substitution nil)
    (ext def-decl "term" substitution nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (unifiable const-decl "bool" unification nil)
    (mgu const-decl "bool" unification nil)
    (unifier const-decl "bool" unification nil)
    (<= const-decl "bool" unification nil)
    (theta!1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs nil)
    (p!1 skolem-const-decl "position[variable, symbol, arity]"
     critical_pairs nil)
    (replaceTerm def-decl "term" replacement nil)
    (rhs const-decl "term" rewrite_rules nil)
    (CP? const-decl "bool" critical_pairs nil)
    (Dom const-decl "set[(V)]" substitution nil)
    (restriction_term formula-decl nil substitution nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (subset? const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (disjoint_subset formula-decl nil IUnion_extra nil)
    (dom_restriction formula-decl nil substitution nil)
    (restriction_Subs formula-decl nil substitution nil)
    (restriction_union formula-decl nil substitution nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (disjoint_commute formula-decl nil IUnion_extra nil)
    (disjoint? const-decl "bool" sets nil)
    (union_commute formula-decl nil substitution nil)
    (rename_preserv_inclusion formula-decl nil substitution nil)
    (same_substitution formula-decl nil substitution nil)
    (same_term formula-decl nil substitution nil)
    (ext_replace_ext formula-decl nil substitution nil)
    (comp const-decl "term" substitution nil)
    (O const-decl "T3" function_props nil)
    (ext_o formula-decl nil substitution nil)
    (U const-decl "set[Sub]" unification nil)
    (e2!1 skolem-const-decl "{e2 | member(e2, E!1)}" critical_pairs
     nil)
    (rho!1 skolem-const-decl "Ren[variable, symbol, arity]"
     critical_pairs nil)
    (alpha!1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs nil)
    (e1!1 skolem-const-decl "{e1 | member(e1, E!1)}" critical_pairs
     nil)
    (E!1 skolem-const-decl "set[rewrite_rule]" critical_pairs nil)
    (sg1!1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs nil)
    (unification formula-decl nil unification nil)
    (vars_subterm formula-decl nil subterm nil)
    (union_is_sub formula-decl nil substitution nil)
    (member const-decl "bool" sets nil)
    (position type-eq-decl nil positions nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil nat_types nil)
    (rewrite_rule type-eq-decl nil rewrite_rules nil)
    (rewrite_rule? const-decl "bool" rewrite_rules nil)
    (Sub type-eq-decl nil substitution nil)
    (Sub? const-decl "bool" substitution nil)
    (V const-decl "set[term]" variables_term nil)
    (set type-eq-decl nil sets nil) (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil))
   shostak))
 (CP_lemma_aux2_TCC1 0
  (CP_lemma_aux2_TCC1-1 nil 3412313494
   ("" (skosimp*)
    (("" (lemma "Pos_var_is_finite")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (Pos_var_is_finite formula-decl nil subterm nil)
    (V const-decl "set[term]" variables_term nil)
    (set type-eq-decl nil sets nil) (term type-decl nil term_adt nil))
   nil))
 (CP_lemma_aux2_TCC2 0
  (CP_lemma_aux2_TCC2-1 nil 3420229945
   ("" (skosimp*)
    (("" (hide (-2 -3))
      (("" (expand "SPP?")
        (("" (split)
          (("1" (grind) nil nil)
           ("2" (expand "SP?")
            (("2" (skosimp*)
              (("2" (expand"#" "finseq_appl")
                (("2" (rewrite "ext_preserv_pos")
                  (("2" (hide 2)
                    (("2" (lemma "set2seq_lem[position]")
                      (("2" (inst?)
                        (("2" (assert)
                          (("2" (replaces -2)
                            (("2" (inst?)
                              (("2"
                                (expand "finseq_appl")
                                (("2"
                                  (expand "Pos_var" -1 1)
                                  (("2"
                                    (expand "extend")
                                    (("2" (propax) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (position type-eq-decl nil positions nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (PP? const-decl "bool" positions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (< const-decl "bool" reals nil) (term type-decl nil term_adt nil)
    (set type-eq-decl nil sets nil)
    (V const-decl "set[term]" variables_term nil)
    (Sub? const-decl "bool" substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (set2seq_lem formula-decl nil set2seq "structures/")
    (below type-eq-decl nil naturalnumbers nil)
    (set2seq def-decl "finite_sequence[T]" set2seq "structures/")
    (Pos_var const-decl "positions" subterm nil)
    (extend const-decl "R" extend nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (positions type-eq-decl nil positions nil)
    (SP? const-decl "bool" positions nil)
    (SPP? const-decl "bool" positions nil))
   nil))
 (CP_lemma_aux2 0
  (CP_lemma_aux2-2 nil 3565130737
   ("" (skolem 1 ("R" "t" "x" "sg1" "sg2"))
    (("" (skoletin* 1)
      (("" (flatten)
        (("" (split)
          (("1" (case "length(seqv) = 0")
            (("1" (hide-all-but (-1 1)) (("1" (grind) nil nil)) nil)
             ("2" (skosimp*)
              (("2" (lemma "CP_lemma_aux2c")
                (("2" (inst -1 "R" "t" "x" "sg1" "sg2" "seqv")
                  (("1" (assert)
                    (("1" (lemma "CP_lemma_aux2d")
                      (("1" (inst -1 "R" "t" "x" "sg1" "sg2")
                        (("1" (assert)
                          (("1" (replace -6 -1 rl)
                            (("1" (replace -5 -1 rl)
                              (("1"
                                (replaces -1)
                                (("1"
                                  (prop)
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (expand"RTC" "IUnion")
                                        (("1"
                                          (inst 2 "length(seqv) - 1")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (skosimp*)
                                    (("2"
                                      (expand "finseq_appl")
                                      (("2"
                                        (lemma "set2seq_lem[position]")
                                        (("2"
                                          (inst -1 "Posv")
                                          (("2"
                                            (assert)
                                            (("2"
                                              (inst?)
                                              (("1"
                                                (expand "finseq_appl")
                                                (("1"
                                                  (replaces -5 -1)
                                                  (("1"
                                                    (expand
                                                     "Pos_var"
                                                     -1
                                                     1)
                                                    (("1"
                                                      (expand "extend")
                                                      (("1"
                                                        (propax)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (typepred "i!2")
                                                (("2"
                                                  (replaces -4)
                                                  (("2"
                                                    (rewrite
                                                     "set2seq_length")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (hide 3)
                    (("2" (expand "SPP?")
                      (("2" (split)
                        (("1" (lemma "pos_occ_var_HAStypePP")
                          (("1" (inst?) (("1" (assertnil nil)) nil))
                          nil)
                         ("2" (lemma "pos_occ_var_HAStypeSP")
                          (("2" (inst?) (("2" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (lemma "CP_lemma_aux2b")
            (("2" (expand "finseq_appl")
              (("2" (inst?)
                (("2" (inst?)
                  (("2" (inst?)
                    (("1" (assert)
                      (("1" (prop)
                        (("1" (lemma "CP_lemma_aux2d")
                          (("1" (inst?)
                            (("1" (inst?)
                              (("1"
                                (assert)
                                (("1"
                                  (expand"RTC" "IUnion")
                                  (("1"
                                    (inst 1 "length(seqv)")
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide 2)
                          (("2" (skosimp*)
                            (("2" (lemma "set2seq_lem[position]")
                              (("2"
                                (inst?)
                                (("2"
                                  (assert)
                                  (("2"
                                    (inst?)
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (replaces -5)
                                        (("1"
                                          (expand "Pos_var" -1 1)
                                          (("1"
                                            (expand "extend")
                                            (("1" (propax) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (typepred "i!1")
                                      (("2"
                                        (replaces -4)
                                        (("2"
                                          (rewrite "set2seq_length")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide 2)
                      (("2" (expand "SPP?")
                        (("2" (split)
                          (("1" (lemma "pos_occ_var_HAStypePP")
                            (("1" (inst?) (("1" (assertnil nil))
                              nil))
                            nil)
                           ("2" (lemma "pos_occ_var_HAStypeSP")
                            (("2" (inst?) (("2" (assertnil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((NOT const-decl "[bool -> bool]" booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (bijective? const-decl "bool" functions nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (TRUE const-decl "bool" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (variable formal-nonempty-type-decl nil critical_pairs nil)
    (symbol formal-nonempty-type-decl nil critical_pairs nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs nil)
    (position type-eq-decl nil positions nil)
    (positions type-eq-decl nil positions nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (term type-decl nil term_adt nil) (set type-eq-decl nil sets nil)
    (V const-decl "set[term]" variables_term nil)
    (Pos_var const-decl "positions" subterm nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (pred type-eq-decl nil defined_types nil)
    (comp_cont? const-decl "bool" compatibility nil)
    (Sub? const-decl "bool" substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (RSigma const-decl "bool" substitution nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (set2seq def-decl "finite_sequence[T]" set2seq "structures/")
    (< const-decl "bool" reals nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (SPP? const-decl "bool" positions nil)
    (ext def-decl "term" substitution nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (reflexive_transitive? const-decl "bool" relations_closure nil)
    (reflexive_transitive type-eq-decl nil relations_closure nil)
    (RTC const-decl "reflexive_transitive" relations_closure nil)
    (SPP type-eq-decl nil positions nil)
    (replace_pos def-decl "term" replace_positions nil)
    (t skolem-const-decl "term[variable, symbol, arity]" critical_pairs
     nil)
    (seqv skolem-const-decl
     "finite_sequence[position[variable, symbol, arity]]"
     critical_pairs nil)
    (CP_lemma_aux2d formula-decl nil critical_pairs_aux nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (i!2 skolem-const-decl "below[length(seqv)]" critical_pairs nil)
    (Card const-decl "nat" finite_sets nil)
    (card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
    (Posv skolem-const-decl "positions[variable, symbol, arity]"
     critical_pairs nil)
    (below type-eq-decl nil naturalnumbers nil)
    (set2seq_length formula-decl nil set2seq "structures/")
    (extend const-decl "R" extend nil)
    (set2seq_lem formula-decl nil set2seq "structures/")
    (pos_occ_var_HAStypeSP formula-decl nil subterm nil)
    (pos_occ_var_HAStypePP formula-decl nil subterm nil)
    (CP_lemma_aux2c formula-decl nil critical_pairs_aux nil)
    (IUnion const-decl "set[T]" indexed_sets nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (^ const-decl "finseq" finite_sequences nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (i!1 skolem-const-decl "below[length(seqv)]" critical_pairs nil)
    (CP_lemma_aux2b formula-decl nil critical_pairs_aux nil))
   nil)
  (CP_lemma_aux2-1 nil 3412011699
   ("" (skolem 1 ("R" "t" "x" "sg1" "sg2"))
    (("" (skoletin* 1)
      (("1" (flatten)
        (("1" (split)
          (("1" (case "length(seqv) = 0")
            (("1" (hide-all-but (-1 1)) (("1" (grind) nil nil)) nil)
             ("2" (skosimp*)
              (("2" (lemma "CP_lemma_aux2c")
                (("2" (inst -1 "R" "t" "x" "sg1" "sg2" "seqv")
                  (("1" (assert)
                    (("1" (lemma "CP_lemma_aux2d")
                      (("1" (inst -1 "R" "t" "x" "sg1" "sg2")
                        (("1" (assert)
                          (("1" (replace -6 -1 rl)
                            (("1" (replace -3 -1 rl)
                              (("1"
                                (replaces -1)
                                (("1"
                                  (prop)
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (expand"RTC" "IUnion")
                                        (("1"
                                          (inst 2 "length(seqv) - 1")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (hide (-2 -3 3))
                                    (("2"
                                      (skosimp*)
                                      (("2"
                                        (expand "finseq_appl")
                                        (("2"
                                          (lemma "fspos.set2seq_lem")
                                          (("2"
                                            (inst -1 "Posv")
                                            (("2"
                                              (assert)
                                              (("2"
                                                (inst?)
                                                (("2"
                                                  (expand
                                                   "finseq_appl")
                                                  (("2"
                                                    (replaces -3 -1)
                                                    (("2"
                                                      (expand
                                                       "Pos_var"
                                                       -1
                                                       1)
                                                      (("2"
                                                        (expand
                                                         "extend")
                                                        (("2"
                                                          (propax)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (hide (-2 -3 3))
                    (("2" (expand "SPP?")
                      (("2" (split)
                        (("1" (lemma "pos_occ_var_HAStypePP")
                          (("1" (inst?) (("1" (assertnil nil)) nil))
                          nil)
                         ("2" (lemma "pos_occ_var_HAStypeSP")
                          (("2" (inst?) (("2" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (lemma "CP_lemma_aux2b")
            (("2" (expand "finseq_appl")
              (("2" (inst?)
                (("2" (inst?)
                  (("2" (inst?)
                    (("1" (assert)
                      (("1" (prop)
                        (("1" (lemma "CP_lemma_aux2d")
                          (("1" (inst?)
                            (("1" (inst?)
                              (("1"
                                (assert)
                                (("1"
                                  (replaces -6)
                                  (("1"
                                    (expand"RTC" "IUnion")
                                    (("1"
                                      (inst 1 "length(seqv)")
                                      (("1"
                                        (replaces -3)
                                        (("1"
                                          (replaces -1 -2)
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide (-3 2))
                          (("2" (skosimp*)
                            (("2" (lemma "fspos.set2seq_lem")
                              (("2"
                                (inst?)
                                (("2"
                                  (assert)
                                  (("2"
                                    (inst?)
                                    (("2"
                                      (expand "finseq_appl")
                                      (("2"
                                        (replaces -4)
                                        (("2"
                                          (expand "Pos_var" -1 1)
                                          (("2"
                                            (expand "extend")
                                            (("2" (propax) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide (-2 -3 2))
                      (("2" (expand "SPP?")
                        (("2" (split)
                          (("1" (lemma "pos_occ_var_HAStypePP")
                            (("1" (inst?) (("1" (assertnil nil))
                              nil))
                            nil)
                           ("2" (lemma "pos_occ_var_HAStypeSP")
                            (("2" (inst?) (("2" (assertnil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (skosimp*)
        (("2" (lemma "CP_lemma_aux2_TCC2")
          (("2" (inst?)
            (("2" (inst?)
              (("2" (assert)
                (("2" (inst?)
                  (("2" (assert) (("2" (inst?) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("3" (skosimp*)
        (("3" (lemma "CP_lemma_aux2_TCC2")
          (("3" (inst?)
            (("3" (inst?)
              (("3" (assert)
                (("3" (inst?)
                  (("3" (assert) (("3" (inst?) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("4" (skosimp*)
        (("4" (lemma "CP_lemma_aux2_TCC1")
          (("4" (inst?)
            (("4" (inst?) (("4" (assert) (("4" (inst?) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (ext def-decl "term" substitution nil)
    (replace_pos def-decl "term" replace_positions nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (RTC const-decl "reflexive_transitive" relations_closure nil)
    (reflexive_transitive type-eq-decl nil relations_closure nil)
    (reflexive_transitive? const-decl "bool" relations_closure nil)
    (RSigma const-decl "bool" substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (Sub? const-decl "bool" substitution nil)
    (comp_cont? const-decl "bool" compatibility nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (position type-eq-decl nil positions nil)
    (positions type-eq-decl nil positions nil)
    (term type-decl nil term_adt nil) (set type-eq-decl nil sets nil)
    (V const-decl "set[term]" variables_term nil)
    (Pos_var const-decl "positions" subterm nil)
    (CP_lemma_aux2d formula-decl nil critical_pairs_aux nil)
    (pos_occ_var_HAStypeSP formula-decl nil subterm nil)
    (pos_occ_var_HAStypePP formula-decl nil subterm nil)
    (CP_lemma_aux2c formula-decl nil critical_pairs_aux nil)
    (^ const-decl "finseq" finite_sequences nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (CP_lemma_aux2b formula-decl nil critical_pairs_aux nil))
   shostak))
 (CP_Theorem 0
  (CP_Theorem-4 nil 3565535039
   ("" (skeep)
    (("" (skoletin* 1)
      (("" (hide -1)
        (("" (split)
          (("1" (flatten)
            (("1" (skeep)
              (("1" (expand "CP?")
                (("1" (skosimp*)
                  (("1" (expand "locally_confluent?")
                    (("1" (inst -1 "ext(sigma!1)(lhs(e1!1))" "t1" "t2")
                      (("1" (assert)
                        (("1" (hide-all-but (-2 -3 -4 1))
                          (("1" (expand "RRE")
                            (("1" (expand "reduction?")
                              (("1"
                                (split)
                                (("1"
                                  (inst 1 "e1!1" "sigma!1" "empty_seq")
                                  (("1"
                                    (split)
                                    (("1"
                                      (expand "subtermOF" 1)
                                      (("1"
                                        (lift-if)
                                        (("1"
                                          (prop)
                                          (("1"
                                            (rewrite "empty_0")
                                            nil
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (expand "replaceTerm" 1)
                                      (("2"
                                        (lift-if)
                                        (("2"
                                          (prop)
                                          (("2"
                                            (rewrite "empty_0")
                                            nil
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (expand "positionsOF")
                                    (("2"
                                      (lift-if)
                                      (("2" (grind) nil nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (inst
                                   1
                                   "e2p!1"
                                   "comp(sigma!1, rho!1)"
                                   "p!1")
                                  (("1"
                                    (rewrite "ext_o")
                                    (("1"
                                      (expand "o")
                                      (("1"
                                        (expand*
                                         "mgu"
                                         "member"
                                         "U"
                                         "unifier")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (lemma
                                             "subterm_ext_commute")
                                            (("1"
                                              (inst
                                               -1
                                               "p!1"
                                               "lhs(e1!1)"
                                               "sigma!1")
                                              (("1"
                                                (typepred "p!1")
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2" (rewrite "subs_o"nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (flatten)
            (("2" (expand "locally_confluent?")
              (("2" (skeep)
                (("2" (expand "RRE")
                  (("2" (expand "reduction?" (-2 -3))
                    (("2" (skosimp*)
                      (("2" (case "parallel(p!1, p!2)")
                        (("1" (hide -2)
                          (("1" (expand "joinable?")
                            (("1"
                              (inst 1
                               "replaceTerm(y, ext(sigma!2)(rhs(e!2)), p!2)")
                              (("1"
                                (expand"RTC" "IUnion")
                                (("1"
                                  (split)
                                  (("1"
                                    (inst 1 "1")
                                    (("1"
                                      (rewrite "iterate_1")
                                      (("1"
                                        (expand "reduction?")
                                        (("1"
                                          (inst
                                           1
                                           "e!2"
                                           "sigma!2"
                                           "p!2")
                                          (("1"
                                            (lemma
                                             "replace_persistence")
                                            (("1"
                                              (inst
                                               -1
                                               "p!1"
                                               "p!2"
                                               "x"
                                               "ext(sigma!1)(rhs(e!1))")
                                              (("1" (assertnil nil))
                                              nil))
                                            nil)
                                           ("2"
                                            (lemma
                                             "replace_preserv_parallel_pos")
                                            (("2"
                                              (inst?)
                                              (("2"
                                                (inst -1 "p!2")
                                                (("2"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (inst 1 "1")
                                    (("2"
                                      (rewrite "iterate_1")
                                      (("2"
                                        (expand "reduction?")
                                        (("2"
                                          (inst
                                           1
                                           "e!1"
                                           "sigma!1"
                                           "p!1")
                                          (("1"
                                            (split)
                                            (("1"
                                              (lemma
                                               "replace_persistence")
                                              (("1"
                                                (inst
                                                 -1
                                                 "p!2"
                                                 "p!1"
                                                 "x"
                                                 "ext(sigma!2)(rhs(e!2))")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (rewrite
                                                     "parallel_comm")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (lemma
                                               "replace_commutativity")
                                              (("2"
                                                (inst
                                                 -1
                                                 "p!1"
                                                 "p!2"
                                                 "ext(sigma!2)(rhs(e!2))"
                                                 "x"
                                                 "ext(sigma!1)(rhs(e!1))")
                                                (("2"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil)
                                           ("2"
                                            (lemma
                                             "replace_preserv_parallel_pos")
                                            (("2"
                                              (inst
                                               -1
                                               "p!2"
                                               "p!1"
                                               "x"
                                               "ext(sigma!2)(rhs(e!2))")
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (rewrite
                                                   "parallel_comm")
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (lemma "replace_preserv_parallel_pos")
                                (("2"
                                  (inst?)
                                  (("2"
                                    (inst -1 "p!2")
                                    (("2" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (expand "parallel")
                          (("2" (expand "<=")
                            (("2" (prop)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (lemma "replace_distributivity")
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (inst
                                       -1
                                       "x"
                                       "ext(sigma!2)(rhs(e!2))")
                                      (("1"
                                        (replace -2 -1 rl)
                                        (("1"
                                          (typepred "p!2")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (replace -8 -2 rl)
                                              (("1"
                                                (replace -5 -2)
                                                (("1"
                                                  (lemma "pos_subterm")
                                                  (("1"
                                                    (inst?)
                                                    (("1"
                                                      (inst -1 "x")
                                                      (("1"
                                                        (replace
                                                         -4
                                                         -1
                                                         rl)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (replace
                                                             -6
                                                             -1)
                                                            (("1"
                                                              (replace
                                                               -1
                                                               -8)
                                                              (("1"
                                                                (lemma
                                                                 "pos_subterm_ax")
                                                                (("1"
                                                                  (inst
                                                                   -1
                                                                   "p!1"
                                                                   "p1!1"
                                                                   "x")
                                                                  (("1"
                                                                    (replace
                                                                     -5
                                                                     -3)
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (replace
                                                                         -7
                                                                         -1)
                                                                        (("1"
                                                                          (lemma
                                                                           "positions_of_ext")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "sigma!1"
                                                                             "lhs(e!1)")
                                                                            (("1"
                                                                              (decompose-equality
                                                                               -1)
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "p1!1")
                                                                                (("1"
                                                                                  (iff)
                                                                                  (("1"
                                                                                    (flatten)
                                                                                    (("1"
                                                                                      (hide
                                                                                       -2)
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (expand*
                                                                                           "union"
                                                                                           "member")
                                                                                          (("1"
                                                                                            (prop)
                                                                                            (("1"
                                                                                              (lemma
                                                                                               "subterm_ext_commute")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -1
                                                                                                 "p1!1"
                                                                                                 "lhs(e!1)"
                                                                                                 "sigma!1")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replaces
                                                                                                     -1)
                                                                                                    (("1"
                                                                                                      (lemma
                                                                                                       "CP_lemma_aux1")
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -1
                                                                                                         "sigma!1"
                                                                                                         "sigma!2"
                                                                                                         "E"
                                                                                                         "p1!1"
                                                                                                         "(lhs(e!1), rhs(e!1))"
                                                                                                         "(lhs(e!2), rhs(e!2))")
                                                                                                        (("1"
                                                                                                          (expand*
                                                                                                           "lhs"
                                                                                                           "rhs")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            (("1"
                                                                                                              (skosimp*)
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 -10
                                                                                                                 "t1!1"
                                                                                                                 "t2!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (replace
                                                                                                                     -8
                                                                                                                     -3
                                                                                                                     rl)
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "joinable?")
                                                                                                                      (("1"
                                                                                                                        (skolem
                                                                                                                         -10
                                                                                                                         "M")
                                                                                                                        (("1"
                                                                                                                          (lemma
                                                                                                                           "reduction_is_subs_op")
                                                                                                                          (("1"
                                                                                                                            (inst?)
                                                                                                                            (("1"
                                                                                                                              (flatten)
                                                                                                                              (("1"
                                                                                                                                (lemma
                                                                                                                                 "closure_close_subs")
                                                                                                                                (("1"
                                                                                                                                  (inst?)
                                                                                                                                  (("1"
                                                                                                                                    (assert)
                                                                                                                                    (("1"
                                                                                                                                      (flatten)
                                                                                                                                      (("1"
                                                                                                                                        (hide
                                                                                                                                         (-1
                                                                                                                                          -3
                                                                                                                                          -4))
                                                                                                                                        (("1"
                                                                                                                                          (expand
                                                                                                                                           "close_subs?")
                                                                                                                                          (("1"
                                                                                                                                            (copy
                                                                                                                                             -1)
                                                                                                                                            (("1"
                                                                                                                                              (inst
                                                                                                                                               -1
                                                                                                                                               "t1!1"
                                                                                                                                               "M"
                                                                                                                                               "delta!1")
                                                                                                                                              (("1"
                                                                                                                                                (inst
                                                                                                                                                 -2
                                                                                                                                                 "t2!1"
                                                                                                                                                 "M"
                                                                                                                                                 "delta!1")
                                                                                                                                                (("1"
                                                                                                                                                  (assert)
                                                                                                                                                  (("1"
                                                                                                                                                    (replaces
                                                                                                                                                     -5)
                                                                                                                                                    (("1"
                                                                                                                                                      (replaces
                                                                                                                                                       -5)
                                                                                                                                                      (("1"
                                                                                                                                                        (lemma
                                                                                                                                                         "comp_op_iff_comp_cont")
                                                                                                                                                        (("1"
                                                                                                                                                          (inst?)
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            (("1"
                                                                                                                                                              (lemma
                                                                                                                                                               "closure_comp_cont")
                                                                                                                                                              (("1"
                                                                                                                                                                (inst?)
                                                                                                                                                                (("1"
                                                                                                                                                                  (assert)
                                                                                                                                                                  (("1"
                                                                                                                                                                    (flatten)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (hide
                                                                                                                                                                       (-1
                                                                                                                                                                        -3
                                                                                                                                                                        -4
                                                                                                                                                                        -7))
                                                                                                                                                                      (("1"
                                                                                                                                                                        (copy
                                                                                                                                                                         -1)
                                                                                                                                                                        (("1"
                                                                                                                                                                          (expand
                                                                                                                                                                           "comp_cont?")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (inst
                                                                                                                                                                             -1
                                                                                                                                                                             "p!1"
                                                                                                                                                                             "x")
                                                                                                                                                                            (("1"
                                                                                                                                                                              (assert)
                                                                                                                                                                              (("1"
                                                                                                                                                                                (inst
                                                                                                                                                                                 -2
                                                                                                                                                                                 "p!1"
                                                                                                                                                                                 "x")
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (assert)
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (inst
                                                                                                                                                                                     -1
                                                                                                                                                                                     "ext(sigma!1)(e!1`2)"
                                                                                                                                                                                     "ext(delta!1)(M)")
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (inst
                                                                                                                                                                                       -2
                                                                                                                                                                                       "subtermOF(z, p!1)"
                                                                                                                                                                                       "ext(delta!1)(M)")
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (assert)
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (lemma
                                                                                                                                                                                           "replace_associativity")
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (inst
                                                                                                                                                                                             -1
                                                                                                                                                                                             "p!1"
                                                                                                                                                                                             "p1!1"
                                                                                                                                                                                             "ext(sigma!2)(e!2`2)"
                                                                                                                                                                                             "x"
                                                                                                                                                                                             "ext(sigma!1)(e!1`1)")
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (assert)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (replace
                                                                                                                                                                                                 -12
                                                                                                                                                                                                 -1
                                                                                                                                                                                                 rl)
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (replace
                                                                                                                                                                                                   -11
                                                                                                                                                                                                   -1
                                                                                                                                                                                                   rl)
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (replace
                                                                                                                                                                                                     -15
                                                                                                                                                                                                     -1
                                                                                                                                                                                                     rl)
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (rewrite
                                                                                                                                                                                                       "replace_subterm_of_term")
                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                        (replace
                                                                                                                                                                                                         -18
                                                                                                                                                                                                         -1
                                                                                                                                                                                                         rl)
                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                          (replace
                                                                                                                                                                                                           -1
                                                                                                                                                                                                           -3
                                                                                                                                                                                                           rl)
                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                            (replace
                                                                                                                                                                                                             -16
                                                                                                                                                                                                             -2
                                                                                                                                                                                                             rl)
                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                              (hide-all-but
                                                                                                                                                                                                               (-2
                                                                                                                                                                                                                -3
                                                                                                                                                                                                                2))
                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                (inst
                                                                                                                                                                                                                 1
                                                                                                                                                                                                                 "replaceTerm(x, ext(delta!1)(M), p!1)")
                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                  (assert)
                                                                                                                                                                                                                  nil
                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                nil))
                                                                                                                                                                                                              nil))
                                                                                                                                                                                                            nil))
                                                                                                                                                                                                          nil))
                                                                                                                                                                                                        nil))
                                                                                                                                                                                                      nil))
                                                                                                                                                                                                    nil))
                                                                                                                                                                                                  nil))
                                                                                                                                                                                                nil))
                                                                                                                                                                                              nil))
                                                                                                                                                                                            nil))
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (typepred
                                                                                                           "e!2")
                                                                                                          (("2"
                                                                                                            (hide-all-but
                                                                                                             (-1
                                                                                                              -2
                                                                                                              1))
                                                                                                            (("2"
                                                                                                              (expand*
                                                                                                               "lhs"
                                                                                                               "rhs"
                                                                                                               "member"
                                                                                                               "rewrite_rule?")
                                                                                                              (("2"
                                                                                                                (prop)
                                                                                                                (("2"
                                                                                                                  (hide-all-but
                                                                                                                   (-2
                                                                                                                    1))
                                                                                                                  (("2"
                                                                                                                    (case-replace
                                                                                                                     "(e!2) = (e!2`1, e!2`2)"
                                                                                                                     :hide?
                                                                                                                     t)
                                                                                                                    (("1"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (decompose-equality
                                                                                                                       1)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("3"
                                                                                                          (typepred
                                                                                                           "e!1")
                                                                                                          (("3"
                                                                                                            (hide-all-but
                                                                                                             (-1
                                                                                                              -2
                                                                                                              1))
                                                                                                            (("3"
                                                                                                              (expand*
                                                                                                               "lhs"
                                                                                                               "rhs"
                                                                                                               "member"
                                                                                                               "rewrite_rule?")
                                                                                                              (("3"
                                                                                                                (case-replace
                                                                                                                 "(e!1) = (e!1`1, e!1`2)"
                                                                                                                 :hide?
                                                                                                                 t)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil)
                                                                                                                 ("2"
                                                                                                                  (decompose-equality
                                                                                                                   1)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil)
                                                                                             ("2"
                                                                                              (skosimp*)
                                                                                              (("2"
                                                                                                (name-replace
                                                                                                 "w"
                                                                                                 "subtermOF(lhs(e!1), p1!2)"
                                                                                                 :hide?
                                                                                                 nil)
                                                                                                (("2"
                                                                                                  (lemma
                                                                                                   "CP_lemma_aux2")
                                                                                                  (("2"
                                                                                                    (inst
                                                                                                     -1
                                                                                                     "reduction?(E)"
                                                                                                     "lhs(e!1)"
                                                                                                     "w"
                                                                                                     "sigma!1"
                                                                                                     "SigmaP(sigma!1, ext(sigma!2)(rhs(e!2)), w, p2!1)")
                                                                                                    (("1"
                                                                                                      (skoletin*
                                                                                                       -1
                                                                                                       :old?
                                                                                                       t)
                                                                                                      (("1"
                                                                                                        (prop)
                                                                                                        (("1"
                                                                                                          (hide
                                                                                                           -2)
                                                                                                          (("1"
                                                                                                            (lemma
                                                                                                             "set2seq_exists[position]")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "Posv"
                                                                                                               "p1!2")
                                                                                                              (("1"
                                                                                                                (replace
                                                                                                                 -3
                                                                                                                 -1
                                                                                                                 rl)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (prop)
                                                                                                                    (("1"
                                                                                                                      (skosimp*)
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "finseq_appl")
                                                                                                                        (("1"
                                                                                                                          (inst
                                                                                                                           -2
                                                                                                                           "ii!1")
                                                                                                                          (("1"
                                                                                                                            (replace
                                                                                                                             -1
                                                                                                                             -2)
                                                                                                                            (("1"
                                                                                                                              (hide
                                                                                                                               (-1
                                                                                                                                -3
                                                                                                                                -4))
                                                                                                                              (("1"
                                                                                                                                (lemma
                                                                                                                                 "CP_lemma_aux2")
                                                                                                                                (("1"
                                                                                                                                  (inst
                                                                                                                                   -1
                                                                                                                                   "reduction?(E)"
                                                                                                                                   "rhs(e!1)"
                                                                                                                                   "w"
                                                                                                                                   "sigma!1"
                                                                                                                                   "SigmaP(sigma!1, ext(sigma!2)(rhs(e!2)), w, p2!1)")
                                                                                                                                  (("1"
                                                                                                                                    (lemma
                                                                                                                                     "set2seq_exists[position]")
                                                                                                                                    (("1"
                                                                                                                                      (inst
                                                                                                                                       -1
                                                                                                                                       "Posv"
                                                                                                                                       "p1!2")
                                                                                                                                      (("1"
                                                                                                                                        (assert)
                                                                                                                                        (("1"
                                                                                                                                          (hide
                                                                                                                                           -1)
                                                                                                                                          (("1"
                                                                                                                                            (prop)
                                                                                                                                            (("1"
                                                                                                                                              (hide
                                                                                                                                               -1)
                                                                                                                                              (("1"
                                                                                                                                                (name-replace
                                                                                                                                                 "SIGMAp"
                                                                                                                                                 "SigmaP(sigma!1, ext(sigma!2)(rhs(e!2)), w, p2!1)")
                                                                                                                                                (("1"
                                                                                                                                                  (case
                                                                                                                                                   "length( #(p1!2)) = 0")
                                                                                                                                                  (("1"
                                                                                                                                                    (hide-all-but
                                                                                                                                                     -1)
                                                                                                                                                    (("1"
                                                                                                                                                      (grind)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil)
                                                                                                                                                   ("2"
                                                                                                                                                    (expand
                                                                                                                                                     "replace_pos"
                                                                                                                                                     -2)
                                                                                                                                                    (("2"
                                                                                                                                                      (assert)
                                                                                                                                                      (("2"
                                                                                                                                                        (expand
                                                                                                                                                         "replace_pos"
                                                                                                                                                         -2)
                                                                                                                                                        (("2"
                                                                                                                                                          (case
                                                                                                                                                           "length(rest( #(p1!2))) = 0")
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            (("1"
                                                                                                                                                              (hide
                                                                                                                                                               -1)
                                                                                                                                                              (("1"
                                                                                                                                                                (expand
                                                                                                                                                                 "SIGMAp"
                                                                                                                                                                 -2
                                                                                                                                                                 1)
                                                                                                                                                                (("1"
                                                                                                                                                                  (expand
                                                                                                                                                                   "ext"
                                                                                                                                                                   -2
                                                                                                                                                                   2)
                                                                                                                                                                  (("1"
                                                                                                                                                                    (expand
                                                                                                                                                                     "SigmaP"
                                                                                                                                                                     -2
                                                                                                                                                                     1)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (lemma
                                                                                                                                                                       "gen_seq_lem[position]")
                                                                                                                                                                      (("1"
                                                                                                                                                                        (inst?)
                                                                                                                                                                        (("1"
                                                                                                                                                                          (expand
                                                                                                                                                                           "finseq_appl")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (replaces
                                                                                                                                                                             -1)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (expand
                                                                                                                                                                               "ext"
                                                                                                                                                                               -7)
                                                                                                                                                                              (("1"
                                                                                                                                                                                (lemma
                                                                                                                                                                                 "ext_preserv_pos")
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (inst
                                                                                                                                                                                   -1
                                                                                                                                                                                   "p1!2"
                                                                                                                                                                                   "lhs(e!1)"
                                                                                                                                                                                   "sigma!1")
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (assert)
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (lemma
                                                                                                                                                                                       "subterm_ext_commute")
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (inst
                                                                                                                                                                                         -1
                                                                                                                                                                                         "p1!2"
                                                                                                                                                                                         "lhs(e!1)"
                                                                                                                                                                                         "sigma!1")
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (assert)
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (replaces
                                                                                                                                                                                             -5
                                                                                                                                                                                             -1)
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (expand
                                                                                                                                                                                               "ext"
                                                                                                                                                                                               -1
                                                                                                                                                                                               2)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (lemma
                                                                                                                                                                                                 "replace_subterm_of_term")
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (inst
                                                                                                                                                                                                   -1
                                                                                                                                                                                                   "p1!2"
                                                                                                                                                                                                   "ext(sigma!1)(lhs(e!1))")
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (assert)
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (replaces
                                                                                                                                                                                                       -2
                                                                                                                                                                                                       -1)
                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                        (lemma
                                                                                                                                                                                                         "replace_associativity")
                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                          (inst
                                                                                                                                                                                                           -1
                                                                                                                                                                                                           "p1!2"
                                                                                                                                                                                                           "p2!1"
                                                                                                                                                                                                           "ext(sigma!2)(rhs(e!2))"
                                                                                                                                                                                                           "ext(sigma!1)(lhs(e!1))"
                                                                                                                                                                                                           "sigma!1(w)")
                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                            (assert)
                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                              (replaces
                                                                                                                                                                                                               -2
                                                                                                                                                                                                               -1)
                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                 -5
                                                                                                                                                                                                                 -1
                                                                                                                                                                                                                 rl)
                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                   -1
                                                                                                                                                                                                                   -4
                                                                                                                                                                                                                   rl)
                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                    (hide
                                                                                                                                                                                                                     -1)
                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                       -11
                                                                                                                                                                                                                       -3
                                                                                                                                                                                                                       rl)
                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                        (case
                                                                                                                                                                                                                         "RTC(reduction?(E))(subtermOF(z, p!1), ext(SIGMAp)(rhs(e!1)))")
                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                          (hide
                                                                                                                                                                                                                           -4)
                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                            (lemma
                                                                                                                                                                                                                             "reduction_is_subs_op")
                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                              (inst?)
                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                (flatten)
                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                  (lemma
                                                                                                                                                                                                                                   "comp_op_iff_comp_cont")
                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                    (inst?)
                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                      (assert)
                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                        (lemma
                                                                                                                                                                                                                                         "closure_comp_cont")
                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                          (inst?)
                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                            (assert)
                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                              (flatten)
                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                (hide
                                                                                                                                                                                                                                                 (-1
                                                                                                                                                                                                                                                  -3
                                                                                                                                                                                                                                                  -4
                                                                                                                                                                                                                                                  -5
                                                                                                                                                                                                                                                  -6))
                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                  (copy
                                                                                                                                                                                                                                                   -1)
                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                    (expand
                                                                                                                                                                                                                                                     "comp_cont?")
                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                      (inst
                                                                                                                                                                                                                                                       -1
                                                                                                                                                                                                                                                       "p!1"
                                                                                                                                                                                                                                                       "x")
                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                        (assert)
                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                          (inst
                                                                                                                                                                                                                                                           -2
                                                                                                                                                                                                                                                           "p!1"
                                                                                                                                                                                                                                                           "x")
                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                            (assert)
                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                              (inst
                                                                                                                                                                                                                                                               -1
                                                                                                                                                                                                                                                               "ext(sigma!1)(e!1`2)"
                                                                                                                                                                                                                                                               "ext(SIGMAp)(rhs(e!1))")
                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                (inst
                                                                                                                                                                                                                                                                 -2
                                                                                                                                                                                                                                                                 "subtermOF(z, p!1)"
                                                                                                                                                                                                                                                                 "ext(SIGMAp)(rhs(e!1))")
                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                  (expand*
                                                                                                                                                                                                                                                                   "rhs"
                                                                                                                                                                                                                                                                   "lhs")
                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                    (assert)
                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                      (lemma
                                                                                                                                                                                                                                                                       "replace_associativity")
                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                        (inst
                                                                                                                                                                                                                                                                         -1
                                                                                                                                                                                                                                                                         "p!1"
                                                                                                                                                                                                                                                                         "p1!1"
                                                                                                                                                                                                                                                                         "ext(sigma!2)(e!2`2)"
                                                                                                                                                                                                                                                                         "x"
                                                                                                                                                                                                                                                                         "ext(sigma!1)(e!1`1)")
                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                          (assert)
                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                                                             -14
                                                                                                                                                                                                                                                                             -1
                                                                                                                                                                                                                                                                             rl)
                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                                                                               -15
                                                                                                                                                                                                                                                                               -1
                                                                                                                                                                                                                                                                               rl)
                                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                                                 -17
                                                                                                                                                                                                                                                                                 -1
                                                                                                                                                                                                                                                                                 rl)
                                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                                  (rewrite
                                                                                                                                                                                                                                                                                   "replace_subterm_of_term")
                                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                                                                     -1
                                                                                                                                                                                                                                                                                     -3
                                                                                                                                                                                                                                                                                     rl)
                                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                                                                                       -20
                                                                                                                                                                                                                                                                                       -3
                                                                                                                                                                                                                                                                                       rl)
                                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                                         -18
                                                                                                                                                                                                                                                                                         -2
                                                                                                                                                                                                                                                                                         rl)
                                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                                          (hide-all-but
                                                                                                                                                                                                                                                                                           (-2
                                                                                                                                                                                                                                                                                            -3
                                                                                                                                                                                                                                                                                            2))
                                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                                            (expand
                                                                                                                                                                                                                                                                                             "joinable?")
                                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                                              (inst
                                                                                                                                                                                                                                                                                               1
                                                                                                                                                                                                                                                                                               "replaceTerm(x, ext(SIGMAp)(e!1`2), p!1)")
                                                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                                                (assert)
                                                                                                                                                                                                                                                                                                nil
                                                                                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                          nil)
                                                                                                                                                                                                                         ("2"
                                                                                                                                                                                                                          (hide-all-but
                                                                                                                                                                                                                           (-3
                                                                                                                                                                                                                            1))
                                                                                                                                                                                                                          (("2"
                                                                                                                                                                                                                            (lemma
                                                                                                                                                                                                                             "reduction_is_subs_op")
                                                                                                                                                                                                                            (("2"
                                                                                                                                                                                                                              (inst?)
                                                                                                                                                                                                                              (("2"
                                                                                                                                                                                                                                (flatten)
                                                                                                                                                                                                                                (("2"
                                                                                                                                                                                                                                  (hide
                                                                                                                                                                                                                                   -2)
                                                                                                                                                                                                                                  (("2"
                                                                                                                                                                                                                                    (lemma
                                                                                                                                                                                                                                     "lhs_reduces_to_rhs")
                                                                                                                                                                                                                                    (("2"
                                                                                                                                                                                                                                      (inst?)
                                                                                                                                                                                                                                      (("2"
                                                                                                                                                                                                                                        (expand
                                                                                                                                                                                                                                         "close_subs?")
                                                                                                                                                                                                                                        (("2"
                                                                                                                                                                                                                                          (inst
                                                                                                                                                                                                                                           -2
                                                                                                                                                                                                                                           "lhs(e!1)"
                                                                                                                                                                                                                                           "rhs(e!1)"
                                                                                                                                                                                                                                           "SIGMAp")
                                                                                                                                                                                                                                          (("2"
                                                                                                                                                                                                                                            (assert)
                                                                                                                                                                                                                                            (("2"
                                                                                                                                                                                                                                              (expand
                                                                                                                                                                                                                                               "RTC")
                                                                                                                                                                                                                                              (("2"
                                                                                                                                                                                                                                                (expand
                                                                                                                                                                                                                                                 "IUnion")
                                                                                                                                                                                                                                                (("2"
                                                                                                                                                                                                                                                  (skosimp*)
                                                                                                                                                                                                                                                  (("2"
                                                                                                                                                                                                                                                    (inst
                                                                                                                                                                                                                                                     1
                                                                                                                                                                                                                                                     "i!1 + 1")
                                                                                                                                                                                                                                                    (("2"
                                                                                                                                                                                                                                                      (expand
                                                                                                                                                                                                                                                       "iterate"
                                                                                                                                                                                                                                                       1)
                                                                                                                                                                                                                                                      (("2"
                                                                                                                                                                                                                                                        (expand
                                                                                                                                                                                                                                                         "o")
                                                                                                                                                                                                                                                        (("2"
                                                                                                                                                                                                                                                          (inst
                                                                                                                                                                                                                                                           1
                                                                                                                                                                                                                                                           "ext(SIGMAp)(lhs(e!1))")
                                                                                                                                                                                                                                                          (("2"
                                                                                                                                                                                                                                                            (assert)
                                                                                                                                                                                                                                                            nil
                                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                                nil))
                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                        nil))
                                                                                                                                                                                                                      nil))
                                                                                                                                                                                                                    nil))
                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                nil))
                                                                                                                                                                                                              nil))
                                                                                                                                                                                                            nil))
                                                                                                                                                                                                          nil))
                                                                                                                                                                                                        nil))
                                                                                                                                                                                                      nil))
                                                                                                                                                                                                    nil))
                                                                                                                                                                                                  nil))
                                                                                                                                                                                                nil))
                                                                                                                                                                                              nil))
                                                                                                                                                                                            nil))
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil)
                                                                                                                                                           ("2"
                                                                                                                                                            (hide-all-but
                                                                                                                                                             1)
                                                                                                                                                            (("2"
                                                                                                                                                              (grind)
                                                                                                                                                              nil
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil)
                                                                                                                                             ("2"
                                                                                                                                              (hide-all-but
                                                                                                                                               1)
                                                                                                                                              (("2"
                                                                                                                                                (lemma
                                                                                                                                                 "reduction_is_subs_op")
                                                                                                                                                (("2"
                                                                                                                                                  (inst?)
                                                                                                                                                  (("2"
                                                                                                                                                    (flatten)
                                                                                                                                                    (("2"
                                                                                                                                                      (lemma
                                                                                                                                                       "comp_op_iff_comp_cont")
                                                                                                                                                      (("2"
                                                                                                                                                        (inst?)
                                                                                                                                                        (("2"
                                                                                                                                                          (assert)
                                                                                                                                                          nil
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil)
                                                                                                                                             ("3"
                                                                                                                                              (hide-all-but
                                                                                                                                               (-2
                                                                                                                                                -3
                                                                                                                                                -4
                                                                                                                                                -5
                                                                                                                                                -6
                                                                                                                                                -7
                                                                                                                                                -8
                                                                                                                                                -9
                                                                                                                                                -11
                                                                                                                                                -15
                                                                                                                                                1))
                                                                                                                                              (("3"
                                                                                                                                                (lemma
                                                                                                                                                 "subterm_of_ext")
                                                                                                                                                (("3"
                                                                                                                                                  (inst
                                                                                                                                                   -1
                                                                                                                                                   "p1!2"
                                                                                                                                                   "p2!1"
                                                                                                                                                   "sigma!1"
                                                                                                                                                   "lhs(e!1)")
                                                                                                                                                  (("3"
                                                                                                                                                    (replace
                                                                                                                                                     -2
                                                                                                                                                     -1)
                                                                                                                                                    (("3"
                                                                                                                                                      (expand
                                                                                                                                                       "ext"
                                                                                                                                                       -1
                                                                                                                                                       (1
                                                                                                                                                        3))
                                                                                                                                                      (("3"
                                                                                                                                                        (expand
                                                                                                                                                         "ext"
                                                                                                                                                         -6)
                                                                                                                                                        (("3"
                                                                                                                                                          (assert)
                                                                                                                                                          (("3"
                                                                                                                                                            (replace
                                                                                                                                                             -3
                                                                                                                                                             -1
                                                                                                                                                             rl)
                                                                                                                                                            (("3"
                                                                                                                                                              (replace
                                                                                                                                                               -11
                                                                                                                                                               -1)
                                                                                                                                                              (("3"
                                                                                                                                                                (lemma
                                                                                                                                                                 "lhs_reduces_to_rhs")
                                                                                                                                                                (("3"
                                                                                                                                                                  (inst?)
                                                                                                                                                                  (("3"
                                                                                                                                                                    (lemma
                                                                                                                                                                     "reduction_is_subs_op")
                                                                                                                                                                    (("3"
                                                                                                                                                                      (inst?)
                                                                                                                                                                      (("3"
                                                                                                                                                                        (flatten)
                                                                                                                                                                        (("3"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "comp_op_iff_comp_cont")
                                                                                                                                                                          (("3"
                                                                                                                                                                            (inst?)
                                                                                                                                                                            (("3"
                                                                                                                                                                              (assert)
                                                                                                                                                                              (("3"
                                                                                                                                                                                (expand
                                                                                                                                                                                 "close_subs?")
                                                                                                                                                                                (("3"
                                                                                                                                                                                  (inst
                                                                                                                                                                                   -2
                                                                                                                                                                                   "lhs(e!2)"
                                                                                                                                                                                   "rhs(e!2)"
                                                                                                                                                                                   "sigma!2")
                                                                                                                                                                                  (("3"
                                                                                                                                                                                    (assert)
                                                                                                                                                                                    (("3"
                                                                                                                                                                                      (replaces
                                                                                                                                                                                       -5)
                                                                                                                                                                                      (("3"
                                                                                                                                                                                        (hide
                                                                                                                                                                                         (-1
                                                                                                                                                                                          -3
                                                                                                                                                                                          -4))
                                                                                                                                                                                        (("3"
                                                                                                                                                                                          (lemma
                                                                                                                                                                                           "SigmaP_is_RSigma")
                                                                                                                                                                                          (("3"
                                                                                                                                                                                            (inst?)
                                                                                                                                                                                            (("3"
                                                                                                                                                                                              (assert)
                                                                                                                                                                                              nil
                                                                                                                                                                                              nil))
                                                                                                                                                                                            nil))
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil)
                                                                                                                                       ("2"
                                                                                                                                        (hide-all-but
                                                                                                                                         1)
                                                                                                                                        (("2"
                                                                                                                                          (expand
                                                                                                                                           "Posv")
                                                                                                                                          (("2"
                                                                                                                                            (lemma
                                                                                                                                             "Pos_var_is_finite")
                                                                                                                                            (("2"
                                                                                                                                              (inst?)
                                                                                                                                              (("2"
                                                                                                                                                (assert)
                                                                                                                                                nil
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (hide-all-but
                                                                                                                       (-4
                                                                                                                        -6
                                                                                                                        -7
                                                                                                                        1))
                                                                                                                      (("2"
                                                                                                                        (expand
                                                                                                                         "Posv")
                                                                                                                        (("2"
                                                                                                                          (lemma
                                                                                                                           "no_empty_set_positions")
                                                                                                                          (("2"
                                                                                                                            (inst?)
                                                                                                                            (("2"
                                                                                                                              (grind)
                                                                                                                              nil
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (hide-all-but
                                                                                                           1)
                                                                                                          (("2"
                                                                                                            (lemma
                                                                                                             "reduction_is_subs_op")
                                                                                                            (("2"
                                                                                                              (inst?)
                                                                                                              (("2"
                                                                                                                (flatten)
                                                                                                                (("2"
                                                                                                                  (lemma
                                                                                                                   "comp_op_iff_comp_cont")
                                                                                                                  (("2"
                                                                                                                    (inst?)
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("3"
                                                                                                          (hide-all-but
                                                                                                           (-3
                                                                                                            -4
                                                                                                            -5
                                                                                                            -6
                                                                                                            -7
                                                                                                            -8
                                                                                                            -9
                                                                                                            -10
                                                                                                            -12
                                                                                                            -16
                                                                                                            1))
                                                                                                          (("3"
                                                                                                            (lemma
                                                                                                             "subterm_of_ext")
                                                                                                            (("3"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "p1!2"
                                                                                                               "p2!1"
                                                                                                               "sigma!1"
                                                                                                               "lhs(e!1)")
                                                                                                              (("3"
                                                                                                                (replace
                                                                                                                 -2
                                                                                                                 -1)
                                                                                                                (("3"
                                                                                                                  (expand
                                                                                                                   "ext"
                                                                                                                   -1
                                                                                                                   (1
                                                                                                                    3))
                                                                                                                  (("3"
                                                                                                                    (expand
                                                                                                                     "ext"
                                                                                                                     -6)
                                                                                                                    (("3"
                                                                                                                      (assert)
                                                                                                                      (("3"
                                                                                                                        (assert)
                                                                                                                        (("3"
                                                                                                                          (replace
                                                                                                                           -3
                                                                                                                           -1
                                                                                                                           rl)
                                                                                                                          (("3"
                                                                                                                            (replace
                                                                                                                             -11
                                                                                                                             -1)
                                                                                                                            (("3"
                                                                                                                              (lemma
                                                                                                                               "lhs_reduces_to_rhs")
                                                                                                                              (("3"
                                                                                                                                (inst?)
                                                                                                                                (("3"
                                                                                                                                  (lemma
                                                                                                                                   "reduction_is_subs_op")
                                                                                                                                  (("3"
                                                                                                                                    (inst?)
                                                                                                                                    (("3"
                                                                                                                                      (flatten)
                                                                                                                                      (("3"
                                                                                                                                        (lemma
                                                                                                                                         "comp_op_iff_comp_cont")
                                                                                                                                        (("3"
                                                                                                                                          (inst?)
                                                                                                                                          (("3"
                                                                                                                                            (assert)
                                                                                                                                            (("3"
                                                                                                                                              (expand
                                                                                                                                               "close_subs?")
                                                                                                                                              (("3"
                                                                                                                                                (inst
                                                                                                                                                 -2
                                                                                                                                                 "lhs(e!2)"
                                                                                                                                                 "rhs(e!2)"
                                                                                                                                                 "sigma!2")
                                                                                                                                                (("3"
                                                                                                                                                  (assert)
                                                                                                                                                  (("3"
                                                                                                                                                    (replaces
                                                                                                                                                     -5)
                                                                                                                                                    (("3"
                                                                                                                                                      (hide
                                                                                                                                                       (-1
                                                                                                                                                        -3
                                                                                                                                                        -4))
                                                                                                                                                      (("3"
                                                                                                                                                        (lemma
                                                                                                                                                         "SigmaP_is_RSigma")
                                                                                                                                                        (("3"
                                                                                                                                                          (inst?)
                                                                                                                                                          (("3"
                                                                                                                                                            (assert)
                                                                                                                                                            nil
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (hide-all-but
                                                                                                       (-5
                                                                                                        -4
                                                                                                        1))
                                                                                                      (("2"
                                                                                                        (expand
                                                                                                         "ext"
                                                                                                         -2)
                                                                                                        (("2"
                                                                                                          (assert)
                                                                                                          (("2"
                                                                                                            (rewrite
                                                                                                             "SigmaP_Subs")
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("3"
                                                                                                      (hide-all-but
                                                                                                       (-5
                                                                                                        -4
                                                                                                        1))
                                                                                                      (("3"
                                                                                                        (expand
                                                                                                         "ext"
                                                                                                         -2)
                                                                                                        (("3"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("4"
                                                                                                      (expand
                                                                                                       "V")
                                                                                                      (("4"
                                                                                                        (propax)
                                                                                                        nil
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                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
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                                                      nil))
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                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (skosimp*)
                                (("2"
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                                  (("2"
                                    (inst?)
                                    (("2"
                                      (inst
                                       -1
                                       "x"
                                       "ext(sigma!1)(rhs(e!1))")
                                      (("2"
                                        (replace -2 -1 rl)
                                        (("2"
                                          (typepred "p!1")
                                          (("2"
                                            (assert)
                                            (("2"
                                              (replace -6 -2 rl)
                                              (("2"
                                                (replace -7 -2)
                                                (("2"
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                                                  (("2"
                                                    (inst?)
                                                    (("2"
                                                      (inst -1 "x")
                                                      (("2"
                                                        (replace
                                                         -4
                                                         -1
                                                         rl)
                                                        (("2"
                                                          (assert)
                                                          (("2"
                                                            (replace
                                                             -8
                                                             -1)
                                                            (("2"
                                                              (replace
                                                               -1
                                                               -6)
                                                              (("2"
                                                                (lemma
                                                                 "pos_subterm_ax")
                                                                (("2"
                                                                  (inst
                                                                   -1
                                                                   "p!2"
                                                                   "p1!1"
                                                                   "x")
                                                                  (("2"
                                                                    (replace
                                                                     -5
                                                                     -3)
                                                                    (("2"
                                                                      (assert)
                                                                      (("2"
                                                                        (replace
                                                                         -9
                                                                         -1)
                                                                        (("2"
                                                                          (lemma
                                                                           "positions_of_ext")
                                                                          (("2"
                                                                            (inst
                                                                             -1
                                                                             "sigma!2"
                                                                             "lhs(e!2)")
                                                                            (("2"
                                                                              (decompose-equality
                                                                               -1)
                                                                              (("2"
                                                                                (inst
                                                                                 -1
                                                                                 "p1!1")
                                                                                (("2"
                                                                                  (iff)
                                                                                  (("2"
                                                                                    (flatten)
                                                                                    (("2"
                                                                                      (hide
                                                                                       -2)
                                                                                      (("2"
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                                                                                        (("2"
                                                                                          (expand*
                                                                                           "union"
                                                                                           "member")
                                                                                          (("2"
                                                                                            (prop)
                                                                                            (("1"
                                                                                              (lemma
                                                                                               "subterm_ext_commute")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -1
                                                                                                 "p1!1"
                                                                                                 "lhs(e!2)"
                                                                                                 "sigma!2")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replaces
                                                                                                     -1)
                                                                                                    (("1"
                                                                                                      (lemma
                                                                                                       "CP_lemma_aux1")
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -1
                                                                                                         "sigma!2"
                                                                                                         "sigma!1"
                                                                                                         "E"
                                                                                                         "p1!1"
                                                                                                         "(lhs(e!2), rhs(e!2))"
                                                                                                         "(lhs(e!1), rhs(e!1))")
                                                                                                        (("1"
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                                                                                                           "lhs"
                                                                                                           "rhs")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            (("1"
                                                                                                              (skosimp*)
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 -10
                                                                                                                 "t1!1"
                                                                                                                 "t2!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (replace
                                                                                                                     -8
                                                                                                                     -3
                                                                                                                     rl)
                                                                                                                    (("1"
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                                                                                                                       "joinable?")
                                                                                                                      (("1"
                                                                                                                        (skolem
                                                                                                                         -10
                                                                                                                         "M")
                                                                                                                        (("1"
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                                                                                                                          (("1"
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                                                                                                                            (("1"
                                                                                                                              (flatten)
                                                                                                                              (("1"
                                                                                                                                (lemma
                                                                                                                                 "closure_close_subs")
                                                                                                                                (("1"
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                                                                                                                                  (("1"
                                                                                                                                    (assert)
                                                                                                                                    (("1"
                                                                                                                                      (flatten)
                                                                                                                                      (("1"
                                                                                                                                        (hide
                                                                                                                                         (-1
                                                                                                                                          -3
                                                                                                                                          -4))
                                                                                                                                        (("1"
                                                                                                                                          (expand
                                                                                                                                           "close_subs?")
                                                                                                                                          (("1"
                                                                                                                                            (copy
                                                                                                                                             -1)
                                                                                                                                            (("1"
                                                                                                                                              (inst
                                                                                                                                               -1
                                                                                                                                               "t1!1"
                                                                                                                                               "M"
                                                                                                                                               "delta!1")
                                                                                                                                              (("1"
                                                                                                                                                (inst
                                                                                                                                                 -2
                                                                                                                                                 "t2!1"
                                                                                                                                                 "M"
                                                                                                                                                 "delta!1")
                                                                                                                                                (("1"
                                                                                                                                                  (assert)
                                                                                                                                                  (("1"
                                                                                                                                                    (replaces
                                                                                                                                                     -5)
                                                                                                                                                    (("1"
                                                                                                                                                      (replaces
                                                                                                                                                       -5)
                                                                                                                                                      (("1"
                                                                                                                                                        (lemma
                                                                                                                                                         "comp_op_iff_comp_cont")
                                                                                                                                                        (("1"
                                                                                                                                                          (inst?)
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            (("1"
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                                                                                                                                                              (("1"
                                                                                                                                                                (inst?)
                                                                                                                                                                (("1"
                                                                                                                                                                  (assert)
                                                                                                                                                                  (("1"
                                                                                                                                                                    (flatten)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (hide
                                                                                                                                                                       (-1
                                                                                                                                                                        -3
                                                                                                                                                                        -4
                                                                                                                                                                        -7))
                                                                                                                                                                      (("1"
                                                                                                                                                                        (copy
                                                                                                                                                                         -1)
                                                                                                                                                                        (("1"
                                                                                                                                                                          (expand
                                                                                                                                                                           "comp_cont?")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (inst
                                                                                                                                                                             -1
                                                                                                                                                                             "p!2"
                                                                                                                                                                             "x")
                                                                                                                                                                            (("1"
                                                                                                                                                                              (assert)
                                                                                                                                                                              (("1"
                                                                                                                                                                                (inst
                                                                                                                                                                                 -2
                                                                                                                                                                                 "p!2"
                                                                                                                                                                                 "x")
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (assert)
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (inst
                                                                                                                                                                                     -1
                                                                                                                                                                                     "ext(sigma!2)(e!2`2)"
                                                                                                                                                                                     "ext(delta!1)(M)")
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (inst
                                                                                                                                                                                       -2
                                                                                                                                                                                       "subtermOF(y, p!2)"
                                                                                                                                                                                       "ext(delta!1)(M)")
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (assert)
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (lemma
                                                                                                                                                                                           "replace_associativity")
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (inst
                                                                                                                                                                                             -1
                                                                                                                                                                                             "p!2"
                                                                                                                                                                                             "p1!1"
                                                                                                                                                                                             "ext(sigma!1)(e!1`2)"
                                                                                                                                                                                             "x"
                                                                                                                                                                                             "ext(sigma!2)(e!2`1)")
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (assert)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (replace
                                                                                                                                                                                                 -12
                                                                                                                                                                                                 -1
                                                                                                                                                                                                 rl)
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (replace
                                                                                                                                                                                                   -11
                                                                                                                                                                                                   -1
                                                                                                                                                                                                   rl)
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (replace
                                                                                                                                                                                                     -17
                                                                                                                                                                                                     -1
                                                                                                                                                                                                     rl)
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (rewrite
                                                                                                                                                                                                       "replace_subterm_of_term")
                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                        (replace
                                                                                                                                                                                                         -16
                                                                                                                                                                                                         -1
                                                                                                                                                                                                         rl)
                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                          (replace
                                                                                                                                                                                                           -1
                                                                                                                                                                                                           -3
                                                                                                                                                                                                           rl)
                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                            (replace
                                                                                                                                                                                                             -18
                                                                                                                                                                                                             -2
                                                                                                                                                                                                             rl)
                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                              (hide-all-but
                                                                                                                                                                                                               (-2
                                                                                                                                                                                                                -3
                                                                                                                                                                                                                2))
                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                (inst
                                                                                                                                                                                                                 1
                                                                                                                                                                                                                 "replaceTerm(x, ext(delta!1)(M), p!2)")
                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                  (assert)
                                                                                                                                                                                                                  nil
                                                                                                                                                                                                                  nil))
                                                                                                                                                                                                                nil))
                                                                                                                                                                                                              nil))
                                                                                                                                                                                                            nil))
                                                                                                                                                                                                          nil))
                                                                                                                                                                                                        nil))
                                                                                                                                                                                                      nil))
                                                                                                                                                                                                    nil))
                                                                                                                                                                                                  nil))
                                                                                                                                                                                                nil))
                                                                                                                                                                                              nil))
                                                                                                                                                                                            nil))
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (typepred
                                                                                                           "e!1")
                                                                                                          (("2"
                                                                                                            (hide-all-but
                                                                                                             (-1
                                                                                                              -2
                                                                                                              1))
                                                                                                            (("2"
                                                                                                              (expand*
                                                                                                               "lhs"
                                                                                                               "rhs"
                                                                                                               "member"
                                                                                                               "rewrite_rule?")
                                                                                                              (("2"
                                                                                                                (prop)
                                                                                                                (("2"
                                                                                                                  (hide-all-but
                                                                                                                   (-2
                                                                                                                    1))
                                                                                                                  (("2"
                                                                                                                    (case-replace
                                                                                                                     "e!1 = (e!1`1, e!1`2)"
                                                                                                                     :hide?
                                                                                                                     t)
                                                                                                                    (("1"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (decompose-equality
                                                                                                                       1)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("3"
                                                                                                          (typepred
                                                                                                           "e!2")
                                                                                                          (("3"
                                                                                                            (hide-all-but
                                                                                                             (-1
                                                                                                              -2
                                                                                                              1))
                                                                                                            (("3"
                                                                                                              (expand*
                                                                                                               "lhs"
                                                                                                               "rhs"
                                                                                                               "member"
                                                                                                               "rewrite_rule?")
                                                                                                              (("3"
                                                                                                                (case-replace
                                                                                                                 "e!2 = (e!2`1, e!2`2)"
                                                                                                                 :hide?
                                                                                                                 t)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil)
                                                                                                                 ("2"
                                                                                                                  (decompose-equality
                                                                                                                   1)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil)
                                                                                             ("2"
                                                                                              (skosimp*)
                                                                                              (("2"
                                                                                                (name-replace
                                                                                                 "w"
                                                                                                 "subtermOF(lhs(e!2), p1!2)"
                                                                                                 :hide?
                                                                                                 nil)
                                                                                                (("2"
                                                                                                  (lemma
                                                                                                   "CP_lemma_aux2")
                                                                                                  (("2"
                                                                                                    (inst
                                                                                                     -1
                                                                                                     "reduction?(E)"
                                                                                                     "lhs(e!2)"
                                                                                                     "w"
                                                                                                     "sigma!2"
                                                                                                     "SigmaP(sigma!2, ext(sigma!1)(rhs(e!1)), w, p2!1)")
                                                                                                    (("1"
                                                                                                      (skoletin*
                                                                                                       -1
                                                                                                       :old?
                                                                                                       t)
                                                                                                      (("1"
                                                                                                        (prop)
                                                                                                        (("1"
                                                                                                          (hide
                                                                                                           -2)
                                                                                                          (("1"
                                                                                                            (lemma
                                                                                                             "set2seq_exists[position]")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "Posv"
                                                                                                               "p1!2")
                                                                                                              (("1"
                                                                                                                (replace
                                                                                                                 -3
                                                                                                                 -1
                                                                                                                 rl)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (prop)
                                                                                                                    (("1"
                                                                                                                      (skosimp*)
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "finseq_appl")
                                                                                                                        (("1"
                                                                                                                          (inst
                                                                                                                           -2
                                                                                                                           "ii!1")
                                                                                                                          (("1"
                                                                                                                            (replace
                                                                                                                             -1
                                                                                                                             -2)
                                                                                                                            (("1"
                                                                                                                              (hide
                                                                                                                               (-1
                                                                                                                                -3
                                                                                                                                -4))
                                                                                                                              (("1"
                                                                                                                                (lemma
                                                                                                                                 "CP_lemma_aux2")
                                                                                                                                (("1"
                                                                                                                                  (inst
                                                                                                                                   -1
                                                                                                                                   "reduction?(E)"
                                                                                                                                   "rhs(e!2)"
                                                                                                                                   "w"
                                                                                                                                   "sigma!2"
                                                                                                                                   "SigmaP(sigma!2, ext(sigma!1)(rhs(e!1)), w, p2!1)")
                                                                                                                                  (("1"
                                                                                                                                    (lemma
                                                                                                                                     "set2seq_exists[position]")
                                                                                                                                    (("1"
                                                                                                                                      (inst
                                                                                                                                       -1
                                                                                                                                       "Posv"
                                                                                                                                       "p1!2")
                                                                                                                                      (("1"
                                                                                                                                        (assert)
                                                                                                                                        (("1"
                                                                                                                                          (hide
                                                                                                                                           -1)
                                                                                                                                          (("1"
                                                                                                                                            (prop)
                                                                                                                                            (("1"
                                                                                                                                              (hide
                                                                                                                                               -1)
                                                                                                                                              (("1"
                                                                                                                                                (name-replace
                                                                                                                                                 "SIGMAp"
                                                                                                                                                 "SigmaP(sigma!2, ext(sigma!1)(rhs(e!1)), w, p2!1)")
                                                                                                                                                (("1"
                                                                                                                                                  (case
                                                                                                                                                   "length( #(p1!2)) = 0")
                                                                                                                                                  (("1"
                                                                                                                                                    (hide-all-but
                                                                                                                                                     -1)
                                                                                                                                                    (("1"
                                                                                                                                                      (grind)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil)
                                                                                                                                                   ("2"
                                                                                                                                                    (expand
                                                                                                                                                     "replace_pos"
                                                                                                                                                     -2)
                                                                                                                                                    (("2"
                                                                                                                                                      (assert)
                                                                                                                                                      (("2"
                                                                                                                                                        (expand
                                                                                                                                                         "replace_pos"
                                                                                                                                                         -2)
                                                                                                                                                        (("2"
                                                                                                                                                          (case
                                                                                                                                                           "length(rest( #(p1!2))) = 0")
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            (("1"
                                                                                                                                                              (hide
                                                                                                                                                               -1)
                                                                                                                                                              (("1"
                                                                                                                                                                (expand
                                                                                                                                                                 "SIGMAp"
                                                                                                                                                                 -2
                                                                                                                                                                 1)
                                                                                                                                                                (("1"
                                                                                                                                                                  (expand
                                                                                                                                                                   "ext"
                                                                                                                                                                   -2
                                                                                                                                                                   2)
                                                                                                                                                                  (("1"
                                                                                                                                                                    (expand
                                                                                                                                                                     "SigmaP"
                                                                                                                                                                     -2
                                                                                                                                                                     1)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (lemma
                                                                                                                                                                       "gen_seq_lem[position]")
                                                                                                                                                                      (("1"
                                                                                                                                                                        (inst?)
                                                                                                                                                                        (("1"
                                                                                                                                                                          (expand
                                                                                                                                                                           "finseq_appl")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (replaces
                                                                                                                                                                             -1)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (expand
                                                                                                                                                                               "ext"
                                                                                                                                                                               -7)
                                                                                                                                                                              (("1"
                                                                                                                                                                                (lemma
                                                                                                                                                                                 "ext_preserv_pos")
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (inst
                                                                                                                                                                                   -1
                                                                                                                                                                                   "p1!2"
                                                                                                                                                                                   "lhs(e!2)"
                                                                                                                                                                                   "sigma!2")
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (assert)
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (lemma
                                                                                                                                                                                       "subterm_ext_commute")
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (inst
                                                                                                                                                                                         -1
                                                                                                                                                                                         "p1!2"
                                                                                                                                                                                         "lhs(e!2)"
                                                                                                                                                                                         "sigma!2")
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (assert)
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (replaces
                                                                                                                                                                                             -5
                                                                                                                                                                                             -1)
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (expand
                                                                                                                                                                                               "ext"
                                                                                                                                                                                               -1
                                                                                                                                                                                               2)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (lemma
                                                                                                                                                                                                 "replace_subterm_of_term")
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (inst
                                                                                                                                                                                                   -1
                                                                                                                                                                                                   "p1!2"
                                                                                                                                                                                                   "ext(sigma!2)(lhs(e!2))")
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (assert)
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (replaces
                                                                                                                                                                                                       -2
                                                                                                                                                                                                       -1)
                                                                                                                                                                                                      (("1"
--> --------------------

--> maximum size reached

--> --------------------

Messung V0.5 in Prozent
C=100 H=100 G=100

¤ Dauer der Verarbeitung: 0.464 Sekunden  (vorverarbeitet am  2026-04-25) ¤

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