Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/TRS/   (Beweissystem der NASA Version 6.0.9©)  Datei vom 28.9.2014 mit Größe 716 kB image not shown  

Quellcode-Bibliothek critical_pairs_aux.prf

  Sprache: Lisp
 

(critical_pairs_aux
 (IMP_rewrite_rules_TCC1 0
  (IMP_rewrite_rules_TCC1-1 nil 3463227045
   ("" (lemma "var_countable") (("" (propax) nil nil)) nil)
   ((var_countable formula-decl nil critical_pairs_aux nil)) nil))
 (CP_lemma_aux2b_TCC1 0
  (CP_lemma_aux2b_TCC1-1 nil 3420220323
   ("" (skosimp*)
    (("" (typepred "fstp!1")
      (("" (expand "SPP?")
        (("" (flatten)
          (("" (assert)
            (("" (hide -1)
              (("" (expand "SP?")
                (("" (skosimp*)
                  (("" (inst -1 "i!1")
                    (("" (expand "finseq_appl")
                      (("" (rewrite "ext_preserv_pos"nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     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)
    (ext_preserv_pos formula-decl nil substitution nil)
    (< const-decl "bool" reals nil)
    (SP? const-decl "bool" positions nil))
   nil))
 (CP_lemma_aux2b_TCC2 0
  (CP_lemma_aux2b_TCC2-1 nil 3455274769 ("" (subtype-tcc) nil 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_aux nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux 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_aux 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)
    (below type-eq-decl nil nat_types nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (position type-eq-decl nil positions nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (SPP? const-decl "bool" positions nil)
    (SPP type-eq-decl nil positions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (injective? const-decl "bool" functions nil)
    (is_finite const-decl "bool" finite_sets nil)
    (SP? const-decl "bool" positions nil)
    (< const-decl "bool" reals nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (CP_lemma_aux2b 0
  (CP_lemma_aux2b-1 nil 3420225063
   ("" (measure-induct+ "length(fstp)" ("t" "fstp"))
    (("1" (skosimp*)
      (("1" (expand "finseq_appl")
        (("1" (case-replace "length(x!2) = 0")
          (("1" (hide-all-but (-1 1))
            (("1" (expand "replace_pos")
              (("1" (lift-if)
                (("1" (assert)
                  (("1" (expand "iterate") (("1" (propax) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (expand "iterate" 2)
            (("2" (prop)
              (("2" (hide 3)
                (("2" (expand "o")
                  (("2"
                    (inst 2
                     "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), delete(x!2,length(x!2) - 1))")
                    (("1" (prop)
                      (("1"
                        (inst -1 "x!1" "delete(x!2, length(x!2) - 1)")
                        (("1" (inst -1 "R!1" "x!3" "sg1!1" "sg2!1")
                          (("1" (prop)
                            (("1"
                              (case "length(delete(x!2, length(x!2) - 1)) = length(x!2) - 1")
                              (("1" (replaces -1) nil nil)
                               ("2"
                                (hide-all-but (1 3))
                                (("2" (grind) nil nil))
                                nil)
                               ("3"
                                (hide-all-but (1 3))
                                (("3" (grind) nil nil))
                                nil))
                              nil)
                             ("2" (hide-all-but (-1 1 3))
                              (("2"
                                (skosimp*)
                                (("2"
                                  (lemma "fspos.delete_pos")
                                  (("2"
                                    (inst?)
                                    (("2"
                                      (assert)
                                      (("2"
                                        (inst -1 "i!1")
                                        (("1"
                                          (inst -2 "i!1")
                                          (("1"
                                            (expand "finseq_appl")
                                            (("1" (assertnil nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide-all-but 1)
                                          (("2"
                                            (typepred "i!1")
                                            (("2" (grind) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("3" (hide-all-but (1 3))
                              (("3" (rewrite "length_delete"nil nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide-all-but (1 3))
                          (("2" (typepred "x!2")
                            (("2" (expand "SPP?")
                              (("2"
                                (flatten)
                                (("2"
                                  (rewrite "delete_of_PP_is_PP")
                                  (("2"
                                    (rewrite "delete_of_SP_is_SP")
                                    nil
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("3" (hide-all-but (1 3))
                          (("3" (grind) nil nil)) nil))
                        nil)
                       ("2" (hide -1)
                        (("2" (lemma "preserv_unchanged_subterms")
                          (("2"
                            (inst -1 "ext(sg2!1)(x!3)"
                             "ext(sg1!1)(x!1)"
                             "delete(x!2, length(x!2) - 1)"
                             "last(x!2)")
                            (("1" (prop)
                              (("1"
                                (lemma "replace_subterm_of_term")
                                (("1"
                                  (inst
                                   -1
                                   "last(x!2)"
                                   "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), delete(x!2, length(x!2) - 1))")
                                  (("1"
                                    (prop)
                                    (("1"
                                      (replaces -2 -1)
                                      (("1"
                                        (expand "last")
                                        (("1"
                                          (expand "finseq_appl")
                                          (("1"
                                            (inst -2 "x!2`length - 1")
                                            (("1"
                                              (lemma
                                               "subterm_ext_commute")
                                              (("1"
                                                (inst
                                                 -1
                                                 "x!2`seq(x!2`length - 1)"
                                                 "x!1"
                                                 "sg1!1")
                                                (("1"
                                                  (prop)
                                                  (("1"
                                                    (replaces -1 -2)
                                                    (("1"
                                                      (replaces -2 -1)
                                                      (("1"
                                                        (expand*
                                                         "comp_cont?"
                                                         "RSigma")
                                                        (("1"
                                                          (inst
                                                           -3
                                                           "x!3")
                                                          (("1"
                                                            (assert)
                                                            (("1"
                                                              (inst
                                                               -2
                                                               "x!2`seq(x!2`length - 1)"
                                                               "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), delete(x!2, length(x!2) - 1))")
                                                              (("1"
                                                                (prop)
                                                                (("1"
                                                                  (inst
                                                                   -1
                                                                   "sg1!1(x!3)"
                                                                   "sg2!1(x!3)")
                                                                  (("1"
                                                                    (assert)
                                                                    (("1"
                                                                      (replace
                                                                       -2
                                                                       1
                                                                       rl)
                                                                      (("1"
                                                                        (hide
                                                                         (-2
                                                                          -3))
                                                                        (("1"
                                                                          (typepred
                                                                           "x!3")
                                                                          (("1"
                                                                            (expand
                                                                             "V")
                                                                            (("1"
                                                                              (expand
                                                                               "ext"
                                                                               1
                                                                               (3
                                                                                5))
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (case-replace
                                                                                   "replace_pos(ext(sg1!1)(x!1), sg2!1(x!3), x!2) = replaceTerm(replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), delete(x!2, length(x!2) - 1)), sg2!1(x!3), x!2`seq(x!2`length - 1))")
                                                                                  (("1"
                                                                                    (hide-all-but
                                                                                     (1
                                                                                      3))
                                                                                    (("1"
                                                                                      (lemma
                                                                                       "fspos.add_last_delete")
                                                                                      (("1"
                                                                                        (inst?)
                                                                                        (("1"
                                                                                          (assert)
                                                                                          (("1"
                                                                                            (name-replace
                                                                                             "RTermTemp"
                                                                                             "replaceTerm(replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), delete(x!2, length(x!2) - 1)), sg2!1(x!3), x!2`seq(x!2`length - 1))")
                                                                                            (("1"
                                                                                              (hide
                                                                                               2)
                                                                                              (("1"
                                                                                                (replaces
                                                                                                 -1)
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "RTermTemp")
                                                                                                  (("1"
                                                                                                    (lemma
                                                                                                     "CP_lemma_aux2a")
                                                                                                    (("1"
                                                                                                      (inst
                                                                                                       -1
                                                                                                       "sg2!1(x!3)"
                                                                                                       "ext(sg1!1)(x!1)"
                                                                                                       "delete(x!2, length(x!2) - 1)"
                                                                                                       "last(x!2)")
                                                                                                      (("1"
                                                                                                        (prop)
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "ext"
                                                                                                           1
                                                                                                           3)
                                                                                                          (("1"
                                                                                                            (expand*
                                                                                                             "last"
                                                                                                             "finseq_appl")
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (hide
                                                                                                           2)
                                                                                                          (("2"
                                                                                                            (case
                                                                                                             "length(x!2) = 1")
                                                                                                            (("1"
                                                                                                              (grind)
                                                                                                              nil
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (skosimp*)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "x!2")
                                                                                                                (("2"
                                                                                                                  (reveal
                                                                                                                   4)
                                                                                                                  (("2"
                                                                                                                    (lemma
                                                                                                                     "fspos.delete_pos")
                                                                                                                    (("2"
                                                                                                                      (expand
                                                                                                                       "finseq_appl")
                                                                                                                      (("2"
                                                                                                                        (inst?)
                                                                                                                        (("2"
                                                                                                                          (assert)
                                                                                                                          (("2"
                                                                                                                            (inst
                                                                                                                             -1
                                                                                                                             "i!1")
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "SPP?")
                                                                                                                              (("1"
                                                                                                                                (flatten)
                                                                                                                                (("1"
                                                                                                                                  (hide
                                                                                                                                   -3)
                                                                                                                                  (("1"
                                                                                                                                    (expand*
                                                                                                                                     "last"
                                                                                                                                     "finseq_appl")
                                                                                                                                    (("1"
                                                                                                                                      (replace
                                                                                                                                       -1
                                                                                                                                       3
                                                                                                                                       rl)
                                                                                                                                      (("1"
                                                                                                                                        (expand
                                                                                                                                         "PP?")
                                                                                                                                        (("1"
                                                                                                                                          (inst
                                                                                                                                           -2
                                                                                                                                           "i!1"
                                                                                                                                           "x!2`length - 1")
                                                                                                                                          (("1"
                                                                                                                                            (expand
                                                                                                                                             "finseq_appl")
                                                                                                                                            (("1"
                                                                                                                                              (assert)
                                                                                                                                              (("1"
                                                                                                                                                (hide
                                                                                                                                                 (-1
                                                                                                                                                  4))
                                                                                                                                                (("1"
                                                                                                                                                  (typepred
                                                                                                                                                   "i!1")
                                                                                                                                                  (("1"
                                                                                                                                                    (grind)
                                                                                                                                                    nil
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil)
                                                                                                                             ("2"
                                                                                                                              (hide-all-but
                                                                                                                               1)
                                                                                                                              (("2"
                                                                                                                                (typepred
                                                                                                                                 "i!1")
                                                                                                                                (("2"
                                                                                                                                  (grind)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide
                                                                                                         2)
                                                                                                        (("2"
                                                                                                          (typepred
                                                                                                           "x!2")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "SPP?")
                                                                                                            (("2"
                                                                                                              (flatten)
                                                                                                              (("2"
                                                                                                                (hide
                                                                                                                 -1)
                                                                                                                (("2"
                                                                                                                  (expand
                                                                                                                   "SP?")
                                                                                                                  (("2"
                                                                                                                    (expand*
                                                                                                                     "last"
                                                                                                                     "finseq_appl")
                                                                                                                    (("2"
                                                                                                                      (inst
                                                                                                                       -1
                                                                                                                       "x!2`length - 1")
                                                                                                                      (("2"
                                                                                                                        (rewrite
                                                                                                                         "ext_preserv_pos")
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
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                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (hide-all-but
                                                                   (1
                                                                    3))
                                                                  (("2"
                                                                    (lemma
                                                                     "preserv_all_parallel_positions")
                                                                    (("2"
                                                                      (inst
                                                                       -1
                                                                       "ext(sg2!1)(x!3)"
                                                                       "ext(sg1!1)(x!1)"
                                                                       "delete(x!2, length(x!2) - 1)"
                                                                       "x!2`seq(x!2`length - 1)")
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (case
                                                                           "length(delete(x!2, length(x!2) - 1)) = 0")
                                                                          (("1"
                                                                            (hide
                                                                             2)
                                                                            (("1"
                                                                              (grind)
                                                                              nil
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide
                                                                             3)
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "x!2")
                                                                                (("2"
                                                                                  (expand
                                                                                   "SPP?")
                                                                                  (("2"
                                                                                    (flatten)
                                                                                    (("2"
                                                                                      (expand
                                                                                       "PP?")
                                                                                      (("2"
                                                                                        (prop)
                                                                                        (("1"
                                                                                          (hide
                                                                                           2)
                                                                                          (("1"
                                                                                            (grind)
                                                                                            nil
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (lemma
                                                                                           "fspos.delete_pos")
                                                                                          (("2"
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                    (("12" (expand "SP?")
                      (("12" (skosimp*)
                        (("12" (inst -1 "i!1")
                          (("12" (rewrite "ext_preserv_pos"nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("13" (hide-all-but 1)
      (("13" (skosimp*)
        (("13" (typepred "y!1`2")
          (("13" (expand "SPP?")
            (("13" (flatten)
              (("13" (hide -1)
                (("13" (expand "SP?") (("13" (inst?) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("14" (hide-all-but 1)
      (("14" (skosimp*)
        (("14" (typepred "fstp!1")
          (("14" (expand "SPP?")
            (("14" (flatten)
              (("14" (hide -1)
                (("14" (expand "SP?") (("14" (inst?) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("15" (hide 2)
      (("15" (typepred "fstp!1")
        (("15" (expand "SPP?")
          (("15" (flatten)
            (("15" (assert)
              (("15" (hide -1)
                (("15" (expand "SP?")
                  (("15" (skosimp*)
                    (("15" (inst -1 "i!1")
                      (("15" (rewrite "ext_preserv_pos"nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((O const-decl "bool" relation_props nil)
    (i!1 skolem-const-decl "below
    [length
       (delete[position[variable, symbol, arity]](x!2, length(x!2) - 1))]"
     critical_pairs_aux nil)
    (PP type-eq-decl nil positions nil)
    (PP? const-decl "bool" positions nil)
    (delete_of_PP_is_PP formula-decl nil positions nil)
    (delete_of_SP_is_SP formula-decl nil positions nil)
    (SP? const-decl "bool" positions nil)
    (SP type-eq-decl nil positions nil)
    (length_delete formula-decl nil seq_extras "structures/")
    (delete_pos formula-decl nil seq_extras "structures/")
    (NOT const-decl "[bool -> bool]" booleans nil)
    (i!1 skolem-const-decl
     "below[length(delete(x!2, length(x!2) - 1))]" critical_pairs_aux
     nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (preserv_unchanged_subterms formula-decl nil replace_positions nil)
    (i!1 skolem-const-decl
     "below[length(delete(x!2, length(x!2) - 1))]" critical_pairs_aux
     nil)
    (subterm_ext_commute formula-decl nil substitution nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (i!1 skolem-const-decl
     "below[length(delete(x!2, length(x!2) - 1))]" critical_pairs_aux
     nil)
    (preserv_all_parallel_positions formula-decl nil replace_positions
     nil)
    (replaceTerm def-decl "term" replacement nil)
    (add_last_delete formula-decl nil seq_extras "structures/")
    (RTermTemp skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (i!1 skolem-const-decl
     "below[length(delete(x!2, length(x!2) - 1))]" critical_pairs_aux
     nil)
    (O const-decl "finseq" finite_sequences nil)
    (<= const-decl "bool" positions nil)
    (parallel const-decl "bool" positions nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (CP_lemma_aux2a formula-decl nil replace_positions nil)
    (replace_subterm_of_term formula-decl nil replacement nil)
    (i!1 skolem-const-decl
     "below[length(delete(x!2, length(x!2) - 1))]" critical_pairs_aux
     nil)
    (last const-decl "T" seq_extras "structures/")
    (not_empty_seq type-eq-decl nil seq_extras "structures/")
    (/= const-decl "boolean" notequal nil)
    (delete const-decl "finseq" seq_extras "structures/")
    (sg1!1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs_aux nil)
    (x!2 skolem-const-decl "SPP[variable, symbol, arity](x!1)"
     critical_pairs_aux nil)
    (x!1 skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (iterate def-decl "pred[[T, T]]" relation_iterate "orders/")
    (RSigma const-decl "bool" substitution nil)
    (comp_cont? const-decl "bool" compatibility nil)
    (subtermOF def-decl "term" subterm nil)
    (positions? type-eq-decl nil positions nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (replace_pos def-decl "term" replace_positions nil)
    (positions type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     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)
    (ext def-decl "term" substitution nil)
    (wf_nat formula-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (naturalnumber type-eq-decl nil naturalnumbers nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux 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_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (measure_induction formula-decl nil measure_induction nil)
    (well_founded? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil))
   shostak))
 (CP_lemma_aux2c1_TCC1 0
  (CP_lemma_aux2c1_TCC1-1 nil 3420220323 ("" (subtype-tcc) nil nil)
   ((NOT const-decl "[bool -> bool]" booleans 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)
    (below type-eq-decl nil nat_types nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (position type-eq-decl nil positions nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (SPP? const-decl "bool" positions nil)
    (SPP type-eq-decl nil positions nil)
    (positions type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions? type-eq-decl nil positions nil)
    (< const-decl "bool" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (injective? const-decl "bool" functions nil)
    (is_finite const-decl "bool" finite_sets nil)
    (SP? const-decl "bool" positions nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (O const-decl "finseq" finite_sequences nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux 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_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (<= const-decl "bool" positions nil)
    (parallel const-decl "bool" positions nil))
   nil))
 (CP_lemma_aux2c1_TCC2 0
  (CP_lemma_aux2c1_TCC2-1 nil 3420220323
   ("" (skolem-typepred)
    (("" (flatten)
      (("" (hide-all-but 1)
        (("" (expand "SPP?")
          (("" (split)
            (("1" (grind) nil nil)
             ("2" (expand"SP?" "nth_seq" "#" "finseq_appl")
              (("2" (skosimp*)
                (("2" (typepred "q!1")
                  (("2" (rewrite "ext_preserv_pos"nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (SP? const-decl "bool" positions nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers 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)
    (positions? type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions type-eq-decl nil positions nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (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_aux nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (CP_lemma_aux2c1_TCC3 0
  (CP_lemma_aux2c1_TCC3-1 nil 3420220323
   ("" (skolem-typepred)
    (("" (skosimp*)
      (("" (expand "SPP?")
        (("" (flatten)
          (("" (split)
            (("1" (rewrite "add_first_parallel_pos_to_PP_is_PP")
              (("1" (hide-all-but (-7 1))
                (("1" (skosimp*)
                  (("1" (inst?)
                    (("1" (expand "finseq_appl")
                      (("1" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (rewrite "add_first_parallel_pos_to_SP_is_SP")
              (("1" (hide-all-but (1 -6))
                (("1" (rewrite "ext_preserv_pos"nil nil)) nil)
               ("2" (hide-all-but (-5 1))
                (("2" (expand "SP?")
                  (("2" (skosimp*)
                    (("2" (inst?)
                      (("2" (rewrite "ext_preserv_pos"nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((add_first_parallel_pos_to_SP_is_SP formula-decl nil positions nil)
    (ext def-decl "term" substitution nil)
    (SP? const-decl "bool" positions nil)
    (SP type-eq-decl nil positions nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (PP type-eq-decl nil positions nil)
    (PP? const-decl "bool" positions nil)
    (add_first_parallel_pos_to_PP_is_PP formula-decl nil positions nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (< const-decl "bool" reals nil)
    (positions? type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions type-eq-decl nil positions nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (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_aux nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (CP_lemma_aux2c1 0
  (CP_lemma_aux2c1-1 nil 3420227790
   ("" (measure-induct+ "length(fst)" ("t" "fst"))
    (("1" (skosimp*)
      (("1" (case "length(x!2) = 0")
        (("1" (hide-all-but (-1 1))
          (("1" (replace -1 1)
            (("1" (rewrite "empty_0")
              (("1" (replaces -1)
                (("1" (rewrite "add_first_empty_seq")
                  (("1" (expand "iterate") (("1" (propax) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (expand "finseq_appl")
          (("2" (inst -1 "x!1" "rest(x!2)")
            (("1" (inst -1 "R!1" "x!3" "sg1!1" "sg2!1" "q!1")
              (("1" (rewrite "length_rest")
                (("1" (prop)
                  (("1"
                    (case-replace "length(rest(x!2)) = length(x!2) -1"
                     :hide? T)
                    (("1" (expand "iterate" 2)
                      (("1" (assert)
                        (("1" (expand "o")
                          (("1"
                            (inst 2
                             "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), add_first(q!1, rest(x!2)))")
                            (("1" (assert)
                              (("1"
                                (hide -1)
                                (("1"
                                  (lemma "CP_lemma_aux2a1")
                                  (("1"
                                    (copy -1)
                                    (("1"
                                      (inst
                                       -1
                                       "ext(sg2!1)(x!3)"
                                       "ext(sg1!1)(x!1)"
                                       "x!2"
                                       "q!1")
                                      (("1"
                                        (inst
                                         -2
                                         "ext(sg2!1)(x!3)"
                                         "ext(sg1!1)(x!1)"
                                         "rest(x!2)"
                                         "q!1")
                                        (("1"
                                          (expand "finseq_appl")
                                          (("1"
                                            (prop)
                                            (("1"
                                              (replaces -1)
                                              (("1"
                                                (replaces -1)
                                                (("1"
                                                  (lemma
                                                   "preserv_unchanged_subterms")
                                                  (("1"
                                                    (inst
                                                     -1
                                                     "ext(sg2!1)(x!3)"
                                                     "ext(sg1!1)(x!1)"
                                                     "rest(x!2)"
                                                     "x!2(0)")
                                                    (("1"
                                                      (expand
                                                       "finseq_appl")
                                                      (("1"
                                                        (prop)
                                                        (("1"
                                                          (lemma
                                                           "replace_subterm_of_term")
                                                          (("1"
                                                            (inst
                                                             -1
                                                             "x!2(0)"
                                                             "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), rest(x!2))")
                                                            (("1"
                                                              (expand
                                                               "finseq_appl")
                                                              (("1"
                                                                (prop)
                                                                (("1"
                                                                  (replaces
                                                                   -2)
                                                                  (("1"
                                                                    (lemma
                                                                     "subterm_ext_commute")
                                                                    (("1"
                                                                      (inst
                                                                       -1
                                                                       "x!2(0)"
                                                                       "x!1"
                                                                       "sg1!1")
                                                                      (("1"
                                                                        (expand
                                                                         "finseq_appl")
                                                                        (("1"
                                                                          (copy
                                                                           -3)
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "0")
                                                                            (("1"
                                                                              (flatten)
                                                                              (("1"
                                                                                (prop)
                                                                                (("1"
                                                                                  (replaces
                                                                                   -3)
                                                                                  (("1"
                                                                                    (replaces
                                                                                     -1)
                                                                                    (("1"
                                                                                      (replace
                                                                                       -2
                                                                                       2
                                                                                       rl)
                                                                                      (("1"
                                                                                        (hide
                                                                                         -2)
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "fspos.seq_first_rest")
                                                                                          (("1"
                                                                                            (inst?)
                                                                                            (("1"
                                                                                              (assert)
                                                                                              (("1"
                                                                                                (expand*
                                                                                                 "first"
                                                                                                 "finseq_appl")
                                                                                                (("1"
                                                                                                  (name-replace
                                                                                                   "RTTemp"
                                                                                                   "replaceTerm(replaceTerm(replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), rest(x!2)), ext(sg1!1)(x!3), x!2`seq(0)), ext(sg2!1)(x!3), q!1)")
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -1
                                                                                                     2)
                                                                                                    (("1"
                                                                                                      (hide
                                                                                                       -1)
                                                                                                      (("1"
                                                                                                        (lemma
                                                                                                         "CP_lemma_aux2a1")
                                                                                                        (("1"
                                                                                                          (inst
                                                                                                           -1
                                                                                                           "ext(sg2!1)(x!3)"
                                                                                                           "ext(sg1!1)(x!1)"
                                                                                                           "rest(x!2)"
                                                                                                           "x!2`seq(0)")
                                                                                                          (("1"
                                                                                                            (prop)
                                                                                                            (("1"
                                                                                                              (replaces
                                                                                                               -1)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "RTTemp")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (lemma
                                                                                                                     "replace_commutativity")
                                                                                                                    (("1"
                                                                                                                      (copy
                                                                                                                       -1)
                                                                                                                      (("1"
                                                                                                                        (name-replace
                                                                                                                         "repTemp"
                                                                                                                         "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), rest(x!2))")
                                                                                                                        (("1"
                                                                                                                          (inst
                                                                                                                           -2
                                                                                                                           "x!2`seq(0)"
                                                                                                                           "q!1"
                                                                                                                           "ext(sg2!1)(x!3)"
                                                                                                                           "repTemp"
                                                                                                                           "ext(sg1!1)(x!3)")
                                                                                                                          (("1"
                                                                                                                            (inst
                                                                                                                             -1
                                                                                                                             "x!2`seq(0)"
                                                                                                                             "q!1"
                                                                                                                             "ext(sg2!1)(x!3)"
                                                                                                                             "repTemp"
                                                                                                                             "ext(sg2!1)(x!3)")
                                                                                                                            (("1"
                                                                                                                              (prop)
                                                                                                                              (("1"
                                                                                                                                (replaces
                                                                                                                                 -1)
                                                                                                                                (("1"
                                                                                                                                  (replaces
                                                                                                                                   -1)
                                                                                                                                  (("1"
                                                                                                                                    (name-replace
                                                                                                                                     "REPLACEtemp"
                                                                                                                                     "replaceTerm(repTemp, ext(sg2!1)(x!3), q!1)")
                                                                                                                                    (("1"
                                                                                                                                      (typepred
                                                                                                                                       "x!3")
                                                                                                                                      (("1"
                                                                                                                                        (expand*
                                                                                                                                         "V"
                                                                                                                                         "ext")
                                                                                                                                        (("1"
                                                                                                                                          (assert)
                                                                                                                                          (("1"
                                                                                                                                            (expand*
                                                                                                                                             "comp_cont?"
                                                                                                                                             "RSigma")
                                                                                                                                            (("1"
                                                                                                                                              (inst
                                                                                                                                               -5
                                                                                                                                               "x!2`seq(0)"
                                                                                                                                               "REPLACEtemp")
                                                                                                                                              (("1"
                                                                                                                                                (inst
                                                                                                                                                 -6
                                                                                                                                                 "x!3")
                                                                                                                                                (("1"
                                                                                                                                                  (prop)
                                                                                                                                                  (("1"
                                                                                                                                                    (inst
                                                                                                                                                     -3
                                                                                                                                                     "sg1!1(x!3)"
                                                                                                                                                     "sg2!1(x!3)")
                                                                                                                                                    (("1"
                                                                                                                                                      (assert)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil)
                                                                                                                                                   ("2"
                                                                                                                                                    (hide
                                                                                                                                                     3)
                                                                                                                                                    (("2"
                                                                                                                                                      (expand
                                                                                                                                                       "REPLACEtemp")
                                                                                                                                                      (("2"
                                                                                                                                                        (expand
                                                                                                                                                         "repTemp")
                                                                                                                                                        (("2"
                                                                                                                                                          (typepred
                                                                                                                                                           "q!1")
                                                                                                                                                          (("2"
                                                                                                                                                            (lemma
                                                                                                                                                             "preserv_all_parallel_positions")
                                                                                                                                                            (("2"
                                                                                                                                                              (inst
                                                                                                                                                               -1
                                                                                                                                                               "ext(sg2!1)(x!3)"
                                                                                                                                                               "ext(sg1!1)(x!1)"
                                                                                                                                                               "rest(x!2)"
                                                                                                                                                               "q!1")
                                                                                                                                                              (("1"
                                                                                                                                                                (prop)
                                                                                                                                                                (("1"
                                                                                                                                                                  (lemma
                                                                                                                                                                   "preserv_all_parallel_positions")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (inst
                                                                                                                                                                     -1
                                                                                                                                                                     "ext(sg2!1)(x!3)"
                                                                                                                                                                     "ext(sg1!1)(x!1)"
                                                                                                                                                                     "rest(x!2)"
                                                                                                                                                                     "x!2`seq(0)")
                                                                                                                                                                    (("1"
                                                                                                                                                                      (prop)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (lemma
                                                                                                                                                                         "replace_preserv_parallel_pos")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (inst
                                                                                                                                                                           -1
                                                                                                                                                                           "q!1"
                                                                                                                                                                           "x!2`seq(0)"
                                                                                                                                                                           "replace_pos(ext(sg1!1)(x!1), ext(sg2!1)(x!3), rest(x!2))"
                                                                                                                                                                           "ext(sg2!1)(x!3)")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (assert)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (hide-all-but
                                                                                                                                                                               (-7
                                                                                                                                                                                1))
                                                                                                                                                                              (("1"
                                                                                                                                                                                (rewrite
                                                                                                                                                                                 "parallel_comm")
                                                                                                                                                                                nil
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil)
                                                                                                                                                                       ("2"
                                                                                                                                                                        (hide-all-but
                                                                                                                                                                         (1
                                                                                                                                                                          3))
                                                                                                                                                                        (("2"
                                                                                                                                                                          (rewrite
                                                                                                                                                                           "rest_parallel_first")
                                                                                                                                                                          nil
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil)
                                                                                                                                                                     ("2"
                                                                                                                                                                      (hide-all-but
                                                                                                                                                                       1)
                                                                                                                                                                      (("2"
                                                                                                                                                                        (typepred
                                                                                                                                                                         "x!2")
                                                                                                                                                                        (("2"
                                                                                                                                                                          (expand*
                                                                                                                                                                           "SPP?"
                                                                                                                                                                           "SP?")
                                                                                                                                                                          (("2"
                                                                                                                                                                            (flatten)
                                                                                                                                                                            (("2"
                                                                                                                                                                              (hide
                                                                                                                                                                               -1)
                                                                                                                                                                              (("2"
                                                                                                                                                                                (inst
                                                                                                                                                                                 -1
                                                                                                                                                                                 "0")
                                                                                                                                                                                (("2"
                                                                                                                                                                                  (expand
                                                                                                                                                                                   "finseq_appl")
                                                                                                                                                                                  (("2"
                                                                                                                                                                                    (rewrite
                                                                                                                                                                                     "ext_preserv_pos")
                                                                                                                                                                                    nil
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil)
                                                                                                                                                                 ("2"
                                                                                                                                                                  (hide-all-but
                                                                                                                                                                   (-6
                                                                                                                                                                    1
                                                                                                                                                                    3))
                                                                                                                                                                  (("2"
                                                                                                                                                                    (skosimp*)
                                                                                                                                                                    (("2"
                                                                                                                                                                      (lemma
                                                                                                                                                                       "rest_parallel_pos_parallel")
                                                                                                                                                                      (("2"
                                                                                                                                                                        (inst?)
                                                                                                                                                                        (("2"
                                                                                                                                                                          (inst
                                                                                                                                                                           -1
                                                                                                                                                                           "q!1")
                                                                                                                                                                          (("2"
                                                                                                                                                                            (prop)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (inst?)
                                                                                                                                                                              nil
                                                                                                                                                                              nil)
                                                                                                                                                                             ("2"
                                                                                                                                                                              (skosimp*)
                                                                                                                                                                              (("2"
                                                                                                                                                                                (inst?)
                                                                                                                                                                                (("2"
                                                                                                                                                                                  (expand
                                                                                                                                                                                   "finseq_appl")
                                                                                                                                                                                  (("2"
                                                                                                                                                                                    (assert)
                                                                                                                                                                                    nil
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil)
                                                                                                                                                               ("2"
                                                                                                                                                                (hide-all-but
                                                                                                                                                                 1)
                                                                                                                                                                (("2"
                                                                                                                                                                  (typepred
                                                                                                                                                                   "q!1")
                                                                                                                                                                  (("2"
                                                                                                                                                                    (rewrite
                                                                                                                                                                     "ext_preserv_pos")
                                                                                                                                                                    nil
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("2"
                                                                                                                                (hide
                                                                                                                                 (-1
                                                                                                                                  3))
                                                                                                                                (("2"
                                                                                                                                  (expand
                                                                                                                                   "repTemp")
                                                                                                                                  (("2"
                                                                                                                                    (rewrite
                                                                                                                                     "preserv_all_parallel_positions")
                                                                                                                                    (("1"
                                                                                                                                      (hide-all-but
                                                                                                                                       (-2
                                                                                                                                        1))
                                                                                                                                      (("1"
                                                                                                                                        (case
                                                                                                                                         "length(rest(x!2)) = 0")
                                                                                                                                        (("1"
                                                                                                                                          (hide
                                                                                                                                           -2)
                                                                                                                                          (("1"
                                                                                                                                            (grind)
                                                                                                                                            nil
                                                                                                                                            nil))
                                                                                                                                          nil)
                                                                                                                                         ("2"
                                                                                                                                          (typepred
                                                                                                                                           "x!2")
                                                                                                                                          (("2"
                                                                                                                                            (expand*
                                                                                                                                             "SPP?"
                                                                                                                                             "PP?")
                                                                                                                                            (("2"
                                                                                                                                              (flatten)
                                                                                                                                              (("2"
                                                                                                                                                (hide
                                                                                                                                                 (-2
                                                                                                                                                  -3))
                                                                                                                                                (("2"
                                                                                                                                                  (prop)
                                                                                                                                                  (("1"
                                                                                                                                                    (grind)
                                                                                                                                                    nil
                                                                                                                                                    nil)
                                                                                                                                                   ("2"
                                                                                                                                                    (skosimp*)
                                                                                                                                                    (("2"
                                                                                                                                                      (inst
                                                                                                                                                       -1
                                                                                                                                                       "i!1 + 1"
                                                                                                                                                       "0")
                                                                                                                                                      (("1"
                                                                                                                                                        (assert)
                                                                                                                                                        (("1"
                                                                                                                                                          (lemma
                                                                                                                                                           "fspos.rest_pos")
                                                                                                                                                          (("1"
                                                                                                                                                            (inst?)
                                                                                                                                                            (("1"
                                                                                                                                                              (assert)
                                                                                                                                                              (("1"
                                                                                                                                                                (inst
                                                                                                                                                                 -1
                                                                                                                                                                 "i!1")
                                                                                                                                                                (("1"
                                                                                                                                                                  (expand
                                                                                                                                                                   "finseq_appl")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (assert)
                                                                                                                                                                    nil
                                                                                                                                                                    nil))
                                                                                                                                                                  nil)
                                                                                                                                                                 ("2"
                                                                                                                                                                  (hide
                                                                                                                                                                   (-1
                                                                                                                                                                    4))
                                                                                                                                                                  (("2"
                                                                                                                                                                    (typepred
                                                                                                                                                                     "i!1")
                                                                                                                                                                    (("2"
                                                                                                                                                                      (grind)
                                                                                                                                                                      nil
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil)
                                                                                                                                                       ("2"
                                                                                                                                                        (hide
                                                                                                                                                         4)
                                                                                                                                                        (("2"
                                                                                                                                                          (typepred
                                                                                                                                                           "i!1")
                                                                                                                                                          (("2"
                                                                                                                                                            (grind)
                                                                                                                                                            nil
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil)
                                                                                                                                     ("2"
                                                                                                                                      (hide-all-but
                                                                                                                                       1)
                                                                                                                                      (("2"
                                                                                                                                        (typepred
                                                                                                                                         "x!2")
                                                                                                                                        (("2"
                                                                                                                                          (expand*
                                                                                                                                           "SPP?"
                                                                                                                                           "SP?")
                                                                                                                                          (("2"
                                                                                                                                            (flatten)
                                                                                                                                            (("2"
                                                                                                                                              (inst
                                                                                                                                               -2
                                                                                                                                               "0")
                                                                                                                                              (("2"
                                                                                                                                                (expand
                                                                                                                                                 "finseq_appl")
                                                                                                                                                (("2"
                                                                                                                                                  (rewrite
                                                                                                                                                   "ext_preserv_pos")
                                                                                                                                                  nil
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("3"
                                                                                                                                (expand
                                                                                                                                 "repTemp")
                                                                                                                                (("3"
                                                                                                                                  (hide-all-but
                                                                                                                                   (-3
                                                                                                                                    1))
                                                                                                                                  (("3"
                                                                                                                                    (rewrite
                                                                                                                                     "preserv_all_parallel_positions")
                                                                                                                                    (("1"
                                                                                                                                      (hide
                                                                                                                                       2)
                                                                                                                                      (("1"
                                                                                                                                        (case
                                                                                                                                         "length(rest(x!2)) = 0")
                                                                                                                                        (("1"
                                                                                                                                          (hide
                                                                                                                                           -2)
                                                                                                                                          (("1"
                                                                                                                                            (grind)
                                                                                                                                            nil
                                                                                                                                            nil))
                                                                                                                                          nil)
                                                                                                                                         ("2"
                                                                                                                                          (skosimp*)
                                                                                                                                          (("2"
                                                                                                                                            (inst
                                                                                                                                             -1
                                                                                                                                             "i!1 + 1")
                                                                                                                                            (("1"
                                                                                                                                              (lemma
                                                                                                                                               "fspos.rest_pos")
                                                                                                                                              (("1"
                                                                                                                                                (expand
                                                                                                                                                 "finseq_appl")
                                                                                                                                                (("1"
                                                                                                                                                  (inst?)
                                                                                                                                                  (("1"
                                                                                                                                                    (assert)
                                                                                                                                                    (("1"
                                                                                                                                                      (inst
                                                                                                                                                       -1
                                                                                                                                                       "i!1")
                                                                                                                                                      (("1"
                                                                                                                                                        (assert)
                                                                                                                                                        nil
                                                                                                                                                        nil)
                                                                                                                                                       ("2"
                                                                                                                                                        (hide
                                                                                                                                                         (-1
                                                                                                                                                          3))
                                                                                                                                                        (("2"
                                                                                                                                                          (typepred
                                                                                                                                                           "i!1")
                                                                                                                                                          (("2"
                                                                                                                                                            (grind)
                                                                                                                                                            nil
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil)
                                                                                                                                             ("2"
                                                                                                                                              (hide
                                                                                                                                               3)
                                                                                                                                              (("2"
                                                                                                                                                (typepred
                                                                                                                                                 "i!1")
                                                                                                                                                (("2"
                                                                                                                                                  (grind)
                                                                                                                                                  nil
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil)
                                                                                                                                     ("2"
                                                                                                                                      (hide
                                                                                                                                       (-1
                                                                                                                                        2))
                                                                                                                                      (("2"
                                                                                                                                        (typepred
                                                                                                                                         "q!1")
                                                                                                                                        (("2"
                                                                                                                                          (rewrite
                                                                                                                                           "ext_preserv_pos")
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("4"
                                                                                                                                (hide
                                                                                                                                 (-1
                                                                                                                                  3))
                                                                                                                                (("4"
                                                                                                                                  (expand
                                                                                                                                   "repTemp")
                                                                                                                                  (("4"
                                                                                                                                    (rewrite
                                                                                                                                     "preserv_all_parallel_positions")
                                                                                                                                    (("1"
                                                                                                                                      (hide-all-but
                                                                                                                                       (1
                                                                                                                                        3))
                                                                                                                                      (("1"
                                                                                                                                        (skosimp*)
                                                                                                                                        (("1"
                                                                                                                                          (typepred
                                                                                                                                           "x!2")
                                                                                                                                          (("1"
                                                                                                                                            (expand
                                                                                                                                             "SPP?")
                                                                                                                                            (("1"
                                                                                                                                              (flatten)
                                                                                                                                              (("1"
                                                                                                                                                (lemma
                                                                                                                                                 "rest_parallel_first")
                                                                                                                                                (("1"
                                                                                                                                                  (inst?)
                                                                                                                                                  (("1"
                                                                                                                                                    (assert)
                                                                                                                                                    nil
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
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                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide-all-but 1)
                                          (("2"
                                            (typepred "q!1")
                                            (("2"
                                              (rewrite
                                               "ext_preserv_pos")
                                              nil
                                              nil))
                                            nil))
                                          nil)
                                         ("3"
                                          (hide-all-but (1 2))
                                          (("3"
                                            (rewrite
                                             "ext_parallel_pos")
                                            (("3"
                                              (hide 2)
                                              (("3"
                                                (typepred "x!2")
                                                (("3"
                                                  (expand "SPP?")
                                                  (("3"
                                                    (flatten)
                                                    (("3"
                                                      (rewrite
                                                       "rest_of_PP_is_PP")
                                                      (("3"
                                                        (rewrite
                                                         "rest_of_SP_is_SP")
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (hide-all-but 1)
                                        (("2"
                                          (typepred "q!1")
                                          (("2"
                                            (rewrite "ext_preserv_pos")
                                            nil
                                            nil))
                                          nil))
                                        nil)
                                       ("3"
                                        (hide-all-but 1)
                                        (("3"
                                          (rewrite "ext_parallel_pos")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide-all-but (1 2)) (("2" (grind) nil nil))
                      nil))
                    nil)
                   ("2" (hide-all-but (-1 1 2))
                    (("2" (case "length(rest(x!2)) = 0")
                      (("1" (hide -2) (("1" (grind) nil nil)) nil)
                       ("2" (skosimp*)
                        (("2" (lemma "fspos.rest_pos")
                          (("2" (inst?)
                            (("2" (assert)
                              (("2"
                                (inst -1 "i!1")
                                (("1"
                                  (expand "finseq_appl")
                                  (("1"
                                    (inst -2 "i!1 + 1")
                                    (("1"
                                      (replace -1 2 rl)
                                      (("1"
                                        (hide -1)
                                        (("1" (assertnil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide (-1 3))
                                      (("2"
                                        (typepred "i!1")
                                        (("2" (grind) nil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (hide (-1 3))
                                  (("2"
                                    (typepred "i!1")
                                    (("2" (grind) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (hide-all-but 1)
              (("2" (typepred "x!2")
                (("2" (expand "SPP?")
                  (("2" (flatten)
                    (("2" (rewrite "rest_of_PP_is_PP")
                      (("2" (rewrite "rest_of_SP_is_SP"nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide-all-but (-1 1))
      (("2" (expand "finseq_appl")
        (("2" (lemma "add_parallel_pos")
          (("2" (inst?)
            (("2" (prop)
              (("2" (hide 2)
                (("2" (skosimp*)
                  (("2" (inst?)
                    (("2" (expand "finseq_appl")
                      (("2" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide-all-but 1)
      (("3" (expand "SPP?")
        (("3" (split)
          (("1" (expand "PP?")
            (("1" (prop) (("1" (hide 2) (("1" (grind) nil nil)) nil))
              nil))
            nil)
           ("2" (typepred "q!1")
            (("2" (expand "SP?")
              (("2" (skosimp*)
                (("2" (expand "finseq_appl")
                  (("2" (lemma "ext_preserv_pos")
                    (("2" (inst?) (("2" (grind) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("4" (hide-all-but 1)
      (("4" (skosimp*)
        (("4" (expand "finseq_appl")
          (("4" (typepred "y!2")
            (("4" (expand"SPP?" "SP?")
              (("4" (flatten)
                (("4" (inst?)
                  (("4" (expand "finseq_appl") (("4" (propax) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("5" (hide-all-but 1)
      (("5" (skosimp*)
        (("5" (hide (-2 -3 -4))
          (("5" (lemma "add_parallel_pos")
            (("5" (inst?)
              (("5" (prop)
                (("5" (hide 2)
                  (("5" (skosimp*)
                    (("5" (expand "finseq_appl")
                      (("5" (inst?) (("5" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("6" (hide (-1 2))
      (("6" (skosimp*)
        (("6" (hide-all-but 1)
          (("6" (expand "SPP?")
            (("6" (split)
              (("1" (expand "PP?")
                (("1" (prop)
                  (("1" (hide 2) (("1" (grind) nil nil)) nil)) nil))
                nil)
               ("2" (expand "SP?")
                (("2" (skosimp*)
                  (("2" (expand "finseq_appl")
                    (("2" (typepred "q!1")
                      (("2" (lemma "ext_preserv_pos")
                        (("2" (inst?) (("2" (grind) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("7" (hide (-1 2))
      (("7" (skosimp*)
        (("7" (hide -1)
          (("7" (expand "finseq_appl")
            (("7" (typepred "y!2")
              (("7" (expand"SPP?" "SP?")
                (("7" (flatten)
                  (("7" (inst?)
                    (("7" (expand "finseq_appl")
                      (("7" (propax) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("8" (hide-all-but 1)
      (("8" (skosimp*)
        (("8" (hide (-2 -3 -4))
          (("8" (lemma "add_parallel_pos")
            (("8" (inst?)
              (("8" (prop)
                (("8" (hide 2)
                  (("8" (skosimp*)
                    (("8" (expand "finseq_appl")
                      (("8" (inst?) (("8" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("9" (hide-all-but (-1 1))
      (("9" (lemma "add_parallel_pos")
        (("9" (inst?)
          (("9" (prop)
            (("9" (hide 2)
              (("9" (skosimp*)
                (("9" (expand "finseq_appl")
                  (("9" (inst?) (("9" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("10" (hide-all-but 1)
      (("10" (expand "SPP?")
        (("10" (split)
          (("1" (expand "PP?")
            (("1" (prop) (("1" (hide 2) (("1" (grind) nil nil)) nil))
              nil))
            nil)
           ("2" (expand "SP?")
            (("2" (skosimp*)
              (("2" (expand "finseq_appl")
                (("2" (typepred "q!1")
                  (("2" (lemma "ext_preserv_pos")
                    (("2" (inst?) (("2" (grind) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("11" (hide-all-but 1)
      (("11" (skosimp*)
        (("11" (hide -1)
          (("11" (typepred "y!1`2")
            (("11" (expand"SPP?" "SP?")
              (("11" (flatten) (("11" (inst?) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("12" (hide-all-but 1)
      (("12" (skosimp*)
        (("12" (hide-all-but 1)
          (("12" (expand "SPP?")
            (("12" (split)
              (("1" (expand "PP?")
                (("1" (prop)
                  (("1" (hide 2) (("1" (grind) nil nil)) nil)) nil))
                nil)
               ("2" (expand "SP?")
                (("2" (skosimp*)
                  (("2" (expand "finseq_appl")
                    (("2" (lemma "ext_preserv_pos")
                      (("2" (inst?) (("2" (grind) nil nil)) nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("13" (hide-all-but (-1 1))
      (("13" (lemma "add_parallel_pos")
        (("13" (inst?)
          (("13" (prop)
            (("13" (hide 2)
              (("13" (skosimp*)
                (("13" (expand "finseq_appl")
                  (("13" (inst?) (("13" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("14" (hide-all-but 1)
      (("14" (expand "SPP?")
        (("14" (split)
          (("1" (expand "PP?")
            (("1" (prop) (("1" (hide 2) (("1" (grind) nil nil)) nil))
              nil))
            nil)
           ("2" (expand "SP?")
            (("2" (skosimp*)
              (("2" (expand "finseq_appl")
                (("2" (typepred "q!1")
                  (("2" (lemma "ext_preserv_pos")
                    (("2" (inst?) (("2" (grind) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("15" (hide-all-but 1)
      (("15" (skosimp*)
        (("15" (hide -1)
          (("15" (typepred "y!1`2")
            (("15" (expand"SPP?" "SP?")
              (("15" (flatten) (("15" (inst?) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("16" (expand "finseq_appl")
      (("16" (hide-all-but 1)
        (("16" (skosimp*)
          (("16" (hide -1)
            (("16" (typepred "x!1`2")
              (("16" (expand"SPP?" "SP?")
                (("16" (flatten)
                  (("16" (inst?)
                    (("16" (expand "finseq_appl")
                      (("16" (propax) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("17" (hide-all-but (-1 1))
      (("17" (lemma "add_parallel_pos")
        (("17" (inst?)
          (("17" (prop)
            (("17" (hide 2)
              (("17" (skosimp*)
                (("17" (expand "finseq_appl")
                  (("17" (inst?) (("17" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("18" (hide-all-but 1)
      (("18" (expand "SPP?")
        (("18" (split)
          (("1" (expand "PP?")
            (("1" (prop) (("1" (hide 2) (("1" (grind) nil nil)) nil))
              nil))
            nil)
           ("2" (expand "SP?")
            (("2" (skosimp*)
              (("2" (expand "finseq_appl")
                (("2" (typepred "q!1")
                  (("2" (lemma "ext_preserv_pos")
                    (("2" (inst?) (("2" (grind) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("19" (hide-all-but 1)
      (("19" (skosimp*)
        (("19" (hide -1)
          (("19" (expand "finseq_appl")
            (("19" (typepred "y!1`2")
              (("19" (expand"SPP?" "SP?")
                (("19" (flatten)
                  (("19" (inst?)
                    (("19" (expand "finseq_appl")
                      (("19" (propax) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("20" (hide-all-but 1)
      (("20" (skosimp*)
        (("20" (hide (-2 -3 -4))
          (("20" (lemma "add_parallel_pos")
            (("20" (inst?)
              (("20" (prop)
                (("20" (hide 2)
                  (("20" (skosimp*)
                    (("20" (expand "finseq_appl")
                      (("20" (inst?) (("20" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("21" (hide-all-but 1)
      (("21" (skosimp*)
        (("21" (hide (-1 -2 -3 -4))
          (("21" (expand "SPP?")
            (("21" (split)
              (("1" (expand "PP?")
                (("1" (prop)
                  (("1" (hide 2) (("1" (grind) nil nil)) nil)) nil))
                nil)
               ("2" (expand "SP?")
                (("2" (skosimp*)
                  (("2" (expand "finseq_appl")
                    (("2" (typepred "q!1")
                      (("2" (lemma "ext_preserv_pos")
                        (("2" (inst?) (("2" (grind) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("22" (hide-all-but 1)
      (("22" (skosimp*)
        (("22" (expand "finseq_appl")
          (("22" (typepred "y!1`2")
            (("22" (expand"SPP?" "SP?")
              (("22" (flatten)
                (("22" (inst?)
                  (("22" (expand "finseq_appl")
                    (("22" (propax) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("23" (hide-all-but (-1 1))
      (("23" (lemma "add_parallel_pos")
        (("23" (inst?)
          (("23" (prop)
            (("23" (hide 2)
              (("23" (skosimp*)
                (("23" (expand "finseq_appl")
                  (("23" (inst?) (("23" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("24" (hide-all-but 1)
      (("24" (expand "SPP?")
        (("24" (split)
          (("1" (expand "PP?")
            (("1" (prop) (("1" (hide 2) (("1" (grind) nil nil)) nil))
              nil))
            nil)
           ("2" (expand "SP?")
            (("2" (skosimp*)
              (("2" (expand "finseq_appl")
                (("2" (typepred "q!1")
                  (("2" (lemma "ext_preserv_pos")
                    (("2" (inst?) (("2" (grind) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("25" (hide-all-but 1)
      (("25" (typepred "fst!1")
        (("25" (expand"SPP?" "SP?")
          (("25" (flatten) (("25" (inst?) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((add_parallel_pos formula-decl nil substitution nil)
    (O const-decl "bool" relation_props nil)
    (CP_lemma_aux2a1 formula-decl nil replace_positions nil)
    (sg1!1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs_aux nil)
    (q!1 skolem-const-decl "positions?[variable, symbol, arity](x!1)"
     critical_pairs_aux nil)
    (preserv_unchanged_subterms formula-decl nil replace_positions nil)
    (replace_subterm_of_term formula-decl nil replacement nil)
    (seq_first_rest formula-decl nil seq_extras "structures/")
    (replaceTerm def-decl "term" replacement nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (REPLACEtemp skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (rest_parallel_pos_parallel formula-decl nil substitution nil)
    (SP? const-decl "bool" positions nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (parallel_comm formula-decl nil positions nil)
    (replace_preserv_parallel_pos formula-decl nil replacement nil)
    (rest_parallel_first formula-decl nil substitution nil)
    (preserv_all_parallel_positions formula-decl nil replace_positions
     nil)
    (repTemp skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (i!1 skolem-const-decl "below[length(rest(x!2))]"
     critical_pairs_aux nil)
    (rest_pos formula-decl nil seq_extras "structures/")
    (int_plus_int_is_int application-judgement "int" integers nil)
    (PP? const-decl "bool" positions nil)
    (<= const-decl "bool" positions nil)
    (O const-decl "finseq" finite_sequences nil)
    (^ const-decl "finseq" finite_sequences nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (i!1 skolem-const-decl "below[length(rest(x!2))]"
     critical_pairs_aux nil)
    (replace_commutativity formula-decl nil replacement nil)
    (RTTemp skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (ext_parallel_pos formula-decl nil substitution nil)
    (SP type-eq-decl nil positions nil)
    (rest_of_SP_is_SP formula-decl nil positions nil)
    (rest_of_PP_is_PP formula-decl nil positions nil)
    (PP type-eq-decl nil positions nil)
    (first const-decl "T" seq_extras "structures/")
    (subterm_ext_commute formula-decl nil substitution nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (i!1 skolem-const-decl "below[length(rest(x!2))]"
     critical_pairs_aux nil)
    (length_rest formula-decl nil seq_extras "structures/")
    (x!2 skolem-const-decl "SPP[variable, symbol, arity](x!1)"
     critical_pairs_aux nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (x!1 skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (empty_0 formula-decl nil seq_extras "structures/")
    (add_first_empty_seq formula-decl nil seq_extras "structures/")
    (replace_pos def-decl "term" replace_positions nil)
    (iterate def-decl "pred[[T, T]]" relation_iterate "orders/")
    (add_first const-decl "finseq" seq_extras "structures/")
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subtermOF def-decl "term" subterm nil)
    (comp_cont? const-decl "bool" compatibility nil)
    (RSigma const-decl "bool" substitution nil)
    (ext def-decl "term" substitution nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (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)
    (positions type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions? type-eq-decl nil positions nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (parallel const-decl "bool" positions nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (wf_nat formula-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (naturalnumber type-eq-decl nil naturalnumbers nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux 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_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (measure_induction formula-decl nil measure_induction nil)
    (well_founded? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil))
   shostak))
 (CP_lemma_aux2c_TCC1 0
  (CP_lemma_aux2c_TCC1-1 nil 3420220323
   ("" (skolem-typepred)
    (("" (flatten)
      (("" (skosimp*)
        (("" (hide (-1 -2 -3))
          (("" (expand "SPP?")
            (("" (flatten)
              (("" (hide -1)
                (("" (expand "SP?") (("" (inst?) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((SP? const-decl "bool" positions nil)
    (< const-decl "bool" reals nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (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_aux nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (CP_lemma_aux2c_TCC2 0
  (CP_lemma_aux2c_TCC2-1 nil 3420220323
   ("" (skolem-typepred)
    (("" (flatten)
      (("" (skosimp*)
        (("" (hide-all-but (-4 2))
          (("" (expand "SPP?")
            (("" (flatten)
              (("" (split)
                (("1" (hide (-1 -2)) (("1" (grind) nil nil)) nil)
                 ("2" (hide -1)
                  (("2" (expand"SP?" "finseq_appl")
                    (("2" (skosimp*)
                      (("2" (expand"#" "finseq_appl")
                        (("2" (inst?)
                          (("2" (rewrite "ext_preserv_pos"nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((< const-decl "bool" reals nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (SP? const-decl "bool" positions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (PP? const-decl "bool" positions nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (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_aux nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (CP_lemma_aux2c_TCC3 0
  (CP_lemma_aux2c_TCC3-1 nil 3420220323 ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux 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_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (comp_cont? const-decl "bool" compatibility nil)
    (RSigma const-decl "bool" substitution nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (CP_lemma_aux2c 0
  (CP_lemma_aux2c-1 nil 3420228904
   ("" (measure-induct+ "length(fstp)" ("t" "fstp"))
    (("1" (skolem 1 ("R" "x" "sg1" "sg2"))
      (("1" (flatten)
        (("1" (skosimp*)
          (("1" (case "length(rest(x!2)) = 0")
            (("1" (hide-all-but (-1 1 2))
              (("1" (lemma "fspos.length_rest_0")
                (("1" (inst?)
                  (("1" (assert)
                    (("1" (replace -1 2)
                      (("1" (typepred "i!1")
                        (("1" (replaces -2 (-1 2))
                          (("1" (expand "finseq_appl")
                            (("1" (expand "replace_pos")
                              (("1"
                                (lift-if)
                                (("1"
                                  (prop)
                                  (("1"
                                    (hide-all-but -1)
                                    (("1" (grind) nil nil))
                                    nil)
                                   ("2"
                                    (case
                                     "length(rest( #(x!2`seq(i!1)))) = 0")
                                    (("1"
                                      (expand "replace_pos")
                                      (("1"
                                        (assert)
                                        (("1"
                                          (hide -1)
                                          (("1"
                                            (expand*
                                             "iterate"
                                             "#"
                                             "finseq_appl")
                                            (("1" (grind) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide-all-but 1)
                                      (("2" (grind) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (expand "finseq_appl")
              (("2" (case-replace "i!1 = 0")
                (("1" (hide -2)
                  (("1" (lemma "CP_lemma_aux2c1")
                    (("1"
                      (inst -1 "R" "x!1" "x" "sg1" "sg2" "rest(x!2)"
                       "x!2`seq(0)")
                      (("1" (prop)
                        (("1" (lemma "fspos.seq_first_rest")
                          (("1" (inst?)
                            (("1" (assert)
                              (("1"
                                (expand"first" "finseq_appl")
                                (("1"
                                  (replace -1 -2 rl)
                                  (("1"
                                    (case-replace
                                     "length(rest(x!2)) = length(x!2) - 1")
                                    (("1"
                                      (hide-all-but (1 2 3))
                                      (("1" (grind) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (skosimp*)
                          (("2" (split)
                            (("1" (hide-all-but (1 2 3))
                              (("1"
                                (expand "finseq_appl")
                                (("1"
                                  (lemma "rest_parallel_first")
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (inst?)
                                        (("1"
                                          (expand "finseq_appl")
                                          (("1" (propax) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (hide-all-but (-2 1 2 3))
                              (("2"
                                (lemma "fspos.rest_pos")
                                (("2"
                                  (inst -1 "x!2")
                                  (("2"
                                    (assert)
                                    (("2"
                                      (inst -1 "i!2")
                                      (("1"
                                        (expand "finseq_appl")
                                        (("1"
                                          (replace -1 1 rl)
                                          (("1"
                                            (inst -2 "i!2 + 1")
                                            (("1" (assertnil nil)
                                             ("2"
                                              (hide (-1 2))
                                              (("2"
                                                (typepred "i!2")
                                                (("2" (grind) nil nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (hide (-1 2))
                                        (("2"
                                          (typepred "i!2")
                                          (("2" (grind) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("3" (hide-all-but (-2 1))
                          (("3" (inst -1 "0"nil nil)) nil))
                        nil)
                       ("2" (hide-all-but 1)
                        (("2" (typepred "x!2")
                          (("2" (expand"SPP?" "SP?")
                            (("2" (flatten)
                              (("2"
                                (inst?)
                                (("2"
                                  (expand "finseq_appl")
                                  (("2" (propax) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("3" (hide-all-but 1)
                        (("3" (typepred "x!2")
                          (("3" (expand "SPP?")
                            (("3" (flatten)
                              (("3"
                                (rewrite "rest_of_PP_is_PP")
                                (("3"
                                  (rewrite "rest_of_SP_is_SP")
                                  nil
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand "iterate" 4)
                  (("2" (prop)
                    (("1" (hide-all-but (-1 3 4))
                      (("1" (grind) nil nil)) nil)
                     ("2" (expand "o")
                      (("2"
                        (inst 2
                         "replace_pos(ext(sg1)(x!1), ext(sg2)(x), rest(x!2))")
                        (("1" (split)
                          (("1" (inst -1 "x!1" "rest(x!2)")
                            (("1" (inst -1 "R" "x" "sg1" "sg2")
                              (("1"
                                (rewrite "length_rest")
                                (("1"
                                  (assert)
                                  (("1"
                                    (prop)
                                    (("1"
                                      (inst -1 "i!1 - 1")
                                      (("1"
                                        (case-replace
                                         "length(rest(x!2)) = length(x!2) - 1"
                                         :hide?
                                         T)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (lemma "fspos.rest_pos")
                                            (("1"
                                              (inst?)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (inst -1 "i!1 - 1")
                                                  (("1"
                                                    (expand
                                                     "finseq_appl")
                                                    (("1"
                                                      (replace
                                                       -1
                                                       -2
                                                       rl)
                                                      (("1"
                                                        (propax)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide-all-but (1 5 6))
                                          (("2" (grind) nil nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (hide-all-but 1)
                                        (("2"
                                          (typepred "i!1")
                                          (("2" (grind) nil nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide-all-but (-1 1 5))
                                      (("2"
                                        (skosimp*)
                                        (("2"
                                          (lemma "fspos.rest_pos")
                                          (("2"
                                            (inst?)
                                            (("2"
                                              (assert)
                                              (("2"
                                                (inst -1 "i!2")
                                                (("1"
                                                  (expand
                                                   "finseq_appl")
                                                  (("1"
                                                    (replace -1 1 rl)
                                                    (("1"
                                                      (inst
                                                       -2
                                                       "1 + i!2")
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (hide (-1 2))
                                                  (("2"
                                                    (typepred "i!2")
                                                    (("2"
                                                      (grind)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (hide-all-but 1)
                              (("2"
                                (typepred "x!2")
                                (("2"
                                  (expand "SPP?")
                                  (("2"
                                    (flatten)
                                    (("2"
                                      (rewrite "rest_of_PP_is_PP")
                                      (("2"
                                        (rewrite "rest_of_SP_is_SP")
                                        nil
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide -1)
                            (("2" (lemma "fspos.seq_first_rest")
                              (("2"
                                (inst?)
                                (("2"
                                  (assert)
                                  (("2"
                                    (name-replace
                                     "RErestTemp"
                                     "replace_pos(ext(sg1)(x!1), ext(sg2)(x), rest(x!2))")
                                    (("2"
                                      (replace -1 1)
                                      (("2"
                                        (expand"first" "finseq_appl")
                                        (("2"
                                          (hide -1)
                                          (("2"
                                            (lemma "CP_lemma_aux2a1")
                                            (("2"
                                              (inst?)
                                              (("1"
                                                (prop)
                                                (("1"
                                                  (replaces -1)
                                                  (("1"
                                                    (expand
                                                     "RErestTemp")
                                                    (("1"
                                                      (lemma
                                                       "preserv_unchanged_subterms")
                                                      (("1"
                                                        (inst
                                                         -1
                                                         "ext(sg2)(x)"
                                                         "ext(sg1)(x!1)"
                                                         "rest(x!2)"
                                                         "x!2`seq(0)")
                                                        (("1"
                                                          (prop)
                                                          (("1"
                                                            (inst
                                                             -2
                                                             "0")
                                                            (("1"
                                                              (lemma
                                                               "subterm_ext_commute")
                                                              (("1"
                                                                (inst
                                                                 -1
                                                                 "x!2`seq(0)"
                                                                 "x!1"
                                                                 "sg1")
                                                                (("1"
                                                                  (prop)
                                                                  (("1"
                                                                    (replaces
                                                                     -3
                                                                     -1)
                                                                    (("1"
                                                                      (replaces
                                                                       -1)
                                                                      (("1"
                                                                        (lemma
                                                                         "replace_subterm_of_term")
                                                                        (("1"
                                                                          (inst
                                                                           -1
                                                                           "x!2`seq(0)"
                                                                           "replace_pos(ext(sg1)(x!1), ext(sg2)(x), rest(x!2))")
                                                                          (("1"
                                                                            (prop)
                                                                            (("1"
                                                                              (replaces
                                                                               -2)
                                                                              (("1"
                                                                                (name-replace
                                                                                 "REPtemp"
                                                                                 "replaceTerm(replace_pos(ext(sg1)(x!1), ext(sg2)(x), rest(x!2)), ext(sg2)(x), x!2`seq(0))")
                                                                                (("1"
                                                                                  (replace
                                                                                   -1
                                                                                   1
                                                                                   rl)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "REPtemp")
                                                                                    (("1"
                                                                                      (hide
                                                                                       -1)
                                                                                      (("1"
                                                                                        (expand*
                                                                                         "comp_cont?"
                                                                                         "RSigma")
                                                                                        (("1"
                                                                                          (typepred
                                                                                           "x")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "V")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "ext"
                                                                                               1
                                                                                               (3
                                                                                                6))
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -2
                                                                                                   "x!2`seq(0)"
                                                                                                   "replace_pos(ext(sg1)(x!1), ext(sg2)(x), rest(x!2))")
                                                                                                  (("1"
                                                                                                    (inst
                                                                                                     -3
                                                                                                     "x")
                                                                                                    (("1"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (hide
                                                                                                         -1)
                                                                                                        (("1"
                                                                                                          (inst
                                                                                                           -2
                                                                                                           "sg1(x)"
                                                                                                           "sg2(x)")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide
                                                                                                         (-1
                                                                                                          -2
                                                                                                          -3
                                                                                                          2))
                                                                                                        (("2"
                                                                                                          (lemma
                                                                                                           "preserv_all_parallel_positions")
                                                                                                          (("2"
                                                                                                            (inst
                                                                                                             -1
                                                                                                             "ext(sg2)(x)"
                                                                                                             "ext(sg1)(x!1)"
                                                                                                             "rest(x!2)"
                                                                                                             "x!2`seq(0)")
                                                                                                            (("1"
                                                                                                              (prop)
                                                                                                              (("1"
                                                                                                                (hide-all-but
                                                                                                                 (1
                                                                                                                  5
                                                                                                                  6))
                                                                                                                (("1"
                                                                                                                  (rewrite
                                                                                                                   "rest_parallel_first")
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (hide-all-but
                                                                                                               1)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "x!2")
                                                                                                                (("2"
                                                                                                                  (expand*
                                                                                                                   "SPP?"
                                                                                                                   "SP?")
                                                                                                                  (("2"
                                                                                                                    (flatten)
                                                                                                                    (("2"
                                                                                                                      (hide
                                                                                                                       -1)
                                                                                                                      (("2"
                                                                                                                        (inst
                                                                                                                         -1
                                                                                                                         "0")
                                                                                                                        (("2"
                                                                                                                          (expand
                                                                                                                           "finseq_appl")
                                                                                                                          (("2"
                                                                                                                            (rewrite
                                                                                                                             "ext_preserv_pos")
                                                                                                                            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
                                                                                5
                                                                                6))
                                                                              (("2"
                                                                                (lemma
                                                                                 "preserv_all_parallel_positions")
                                                                                (("2"
                                                                                  (inst
                                                                                   -1
                                                                                   "ext(sg2)(x)"
                                                                                   "ext(sg1)(x!1)"
                                                                                   "rest(x!2)"
                                                                                   "x!2`seq(0)")
                                                                                  (("1"
                                                                                    (prop)
                                                                                    (("1"
                                                                                      (hide-all-but
                                                                                       1)
                                                                                      (("1"
                                                                                        (rewrite
                                                                                         "rest_parallel_first")
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     1)
                                                                                    (("2"
                                                                                      (typepred
                                                                                       "x!2")
                                                                                      (("2"
                                                                                        (expand*
                                                                                         "SPP?"
                                                                                         "SP?")
                                                                                        (("2"
                                                                                          (flatten)
                                                                                          (("2"
                                                                                            (hide
                                                                                             -1)
                                                                                            (("2"
                                                                                              (inst
                                                                                               -1
                                                                                               "0")
                                                                                              (("2"
                                                                                                (expand
                                                                                                 "finseq_appl")
                                                                                                (("2"
                                                                                                  (rewrite
                                                                                                   "ext_preserv_pos")
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide-all-but
                                                                     1)
                                                                    (("2"
                                                                      (typepred
                                                                       "x!2")
                                                                      (("2"
                                                                        (expand*
                                                                         "SPP?"
                                                                         "SP?")
                                                                        (("2"
                                                                          (flatten)
                                                                          (("2"
                                                                            (hide
                                                                             -1)
                                                                            (("2"
                                                                              (inst
                                                                               -1
                                                                               "0")
                                                                              (("2"
                                                                                (expand
                                                                                 "finseq_appl")
                                                                                (("2"
                                                                                  (propax)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (hide-all-but
                                                             1)
                                                            (("2"
                                                              (rewrite
                                                               "rest_parallel_first")
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("2"
                                                          (hide-all-but
                                                           1)
                                                          (("2"
                                                            (typepred
                                                             "x!2")
                                                            (("2"
                                                              (expand*
                                                               "SPP?"
                                                               "SP?")
                                                              (("2"
                                                                (flatten)
                                                                (("2"
                                                                  (hide
                                                                   -1)
                                                                  (("2"
                                                                    (inst
                                                                     -1
                                                                     "0")
                                                                    (("2"
                                                                      (expand
                                                                       "finseq_appl")
                                                                      (("2"
                                                                        (rewrite
                                                                         "ext_preserv_pos")
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (hide-all-but 1)
                                                  (("2"
                                                    (rewrite
                                                     "rest_parallel_first")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (hide-all-but 1)
                                                (("2"
                                                  (typepred "x!2")
                                                  (("2"
                                                    (expand*
                                                     "SPP?"
                                                     "SP?")
                                                    (("2"
                                                      (flatten)
                                                      (("2"
                                                        (hide -1)
                                                        (("2"
                                                          (inst -1 "0")
                                                          (("2"
                                                            (expand
                                                             "finseq_appl")
                                                            (("2"
                                                              (rewrite
                                                               "ext_preserv_pos")
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("3"
                                                (hide-all-but (1 5 6))
                                                (("3"
                                                  (typepred "x!2")
                                                  (("3"
                                                    (expand "SPP?")
                                                    (("3"
                                                      (flatten)
                                                      (("3"
                                                        (rewrite
                                                         "rest_of_PP_is_PP")
                                                        (("3"
                                                          (hide -1)
                                                          (("3"
                                                            (expand
                                                             "SP?")
                                                            (("3"
                                                              (skosimp*)
                                                              (("3"
                                                                (lemma
                                                                 "fspos.rest_pos")
                                                                (("3"
                                                                  (inst?)
                                                                  (("3"
                                                                    (assert)
                                                                    (("3"
                                                                      (inst
                                                                       -1
                                                                       "i!2")
                                                                      (("1"
                                                                        (expand
                                                                         "finseq_appl")
                                                                        (("1"
                                                                          (replace
                                                                           -1
                                                                           1
                                                                           rl)
                                                                          (("1"
                                                                            (hide
                                                                             -1)
                                                                            (("1"
                                                                              (inst
                                                                               -1
                                                                               "1 + i!2")
                                                                              (("1"
                                                                                (rewrite
                                                                                 "ext_preserv_pos")
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (hide
                                                                         (-1
                                                                          2))
                                                                        (("2"
                                                                          (typepred
                                                                           "i!2")
                                                                          (("2"
                                                                            (grind)
                                                                            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 4 5))
                          (("2" (rewrite "ext_parallel_pos")
                            (("2" (hide 2)
                              (("2"
                                (typepred "x!2")
                                (("2"
                                  (expand "SPP?")
                                  (("2"
                                    (flatten)
                                    (("2"
                                      (rewrite "rest_of_PP_is_PP")
                                      (("2"
                                        (rewrite "rest_of_SP_is_SP")
                                        nil
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide-all-but 2)
      (("2" (skosimp*)
        (("2" (typepred "y!2")
          (("2" (expand"SPP?" "SP?")
            (("2" (flatten)
              (("2" (assert)
                (("2" (skosimp*)
                  (("2" (expand "finseq_appl")
                    (("2" (inst?)
                      (("2" (hide -1)
                        (("2" (rewrite "ext_preserv_pos"nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide-all-but 2)
      (("3" (skosimp*)
        (("3" (typepred "y!2")
          (("3" (expand "SPP?")
            (("3" (flatten)
              (("3" (split)
                (("1" (hide (-1 -2))
                  (("1" (expand "PP?")
                    (("1" (prop)
                      (("1" (hide 2) (("1" (grind) nil nil)) nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide -1)
                  (("2" (expand "SP?")
                    (("2" (skosimp*)
                      (("2" (expand "finseq_appl")
                        (("2" (inst?)
                          (("2" (lemma "ext_preserv_pos")
                            (("2" (inst?) (("2" (grind) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("4" (hide-all-but 2)
      (("4" (skosimp*)
        (("4" (typepred "y!2")
          (("4" (expand"SPP?" "SP?")
            (("4" (flatten) (("4" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
      nil)
     ("5" (hide-all-but 1)
      (("5" (skosimp*)
        (("5" (hide (-2 -3))
          (("5" (lemma "ext_parallel_pos") (("5" (inst?) nil nil))
            nil))
          nil))
        nil))
      nil)
     ("6" (hide-all-but 1)
      (("6" (skosimp*)
        (("6" (hide-all-but 2)
          (("6" (typepred "y!2")
            (("6" (expand "SPP?")
              (("6" (flatten)
                (("6" (split)
                  (("1" (expand "PP?")
                    (("1" (prop)
                      (("1" (hide 2) (("1" (grind) nil nil)) nil)
                       ("2" (hide 3) (("2" (grind) nil nil)) nil))
                      nil))
                    nil)
                   ("2" (hide -1)
                    (("2" (expand "SP?")
                      (("2" (skosimp*)
                        (("2" (expand "finseq_appl")
                          (("2" (inst?)
                            (("2" (lemma "ext_preserv_pos")
                              (("2"
                                (inst?)
                                (("2" (grind) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("7" (hide-all-but 1)
      (("7" (skosimp*)
        (("7" (typepred "y!2")
          (("7" (expand"SPP?" "SP?")
            (("7" (flatten) (("7" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
      nil)
     ("8" (hide-all-but 1)
      (("8" (skosimp*)
        (("8" (hide-all-but 2)
          (("8" (typepred "x!1`2")
            (("8" (lemma "ext_parallel_pos") (("8" (inst?) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("9" (hide-all-but 2)
      (("9" (skosimp*)
        (("9" (typepred "y!1`2")
          (("9" (lemma "ext_parallel_pos") (("9" (inst?) nil nil))
            nil))
          nil))
        nil))
      nil)
     ("10" (hide-all-but 2)
      (("10" (skosimp*)
        (("10" (typepred "y!1`2")
          (("10" (expand "SPP?")
            (("10" (flatten)
              (("10" (split)
                (("1" (expand "PP?")
                  (("1" (prop)
                    (("1" (hide 2) (("1" (grind) nil nil)) nil)
                     ("2" (hide 3) (("2" (grind) nil nil)) nil))
                    nil))
                  nil)
                 ("2" (hide -1)
                  (("2" (expand "SP?")
                    (("2" (skosimp*)
                      (("2" (expand "finseq_appl")
                        (("2" (inst?)
                          (("2" (lemma "ext_preserv_pos")
                            (("2" (inst?) (("2" (grind) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
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                nil))
              nil))
            nil))
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        nil))
      nil)
     ("11" (hide-all-but 2)
      (("11" (skosimp*)
        (("11" (typepred "y!1`2")
          (("11" (expand"SPP?" "SP?")
            (("11" (flatten) (("11" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
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     ("12" (hide-all-but 1)
      (("12" (skosimp*)
        (("12" (hide (-2 -3))
          (("12" (typepred "x!1`2")
            (("12" (expand "SPP?")
              (("12" (flatten)
                (("12" (split)
                  (("1" (expand "PP?")
                    (("1" (prop)
                      (("1" (hide 2) (("1" (grind) nil nil)) nil)
                       ("2" (hide 3) (("2" (grind) nil nil)) nil))
                      nil))
                    nil)
                   ("2" (hide -1)
                    (("2" (expand "SP?")
                      (("2" (skosimp*)
                        (("2" (expand "finseq_appl")
                          (("2" (inst?)
                            (("2" (lemma "ext_preserv_pos")
                              (("2"
                                (inst?)
                                (("2" (grind) nil nil))
                                nil))
                              nil))
                            nil))
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     ("13" (hide-all-but 2)
      (("13" (skosimp*)
        (("13" (lemma "ext_parallel_pos") (("13" (inst?) nil nil))
          nil))
        nil))
      nil)
     ("14" (hide-all-but 2)
      (("14" (skosimp*)
        (("14" (typepred "y!1`2")
          (("14" (expand "SPP?")
            (("14" (flatten)
              (("14" (split)
                (("1" (expand "PP?")
                  (("1" (prop)
                    (("1" (hide 2) (("1" (grind) nil nil)) nil)
                     ("2" (hide 3) (("2" (grind) nil nil)) nil))
                    nil))
                  nil)
                 ("2" (hide -1)
                  (("2" (expand "SP?")
                    (("2" (skosimp*)
                      (("2" (expand "finseq_appl")
                        (("2" (inst?)
                          (("2" (lemma "ext_preserv_pos")
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                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("15" (hide-all-but 2)
      (("15" (skosimp*)
        (("15" (typepred "y!1`2")
          (("15" (expand"SPP?" "SP?")
            (("15" (flatten) (("15" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
      nil)
     ("16" (hide-all-but 1)
      (("16" (skosimp*)
        (("16" (typepred "x!1`2")
          (("16" (expand"SPP?" "SP?")
            (("16" (flatten) (("16" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
      nil)
     ("17" (hide-all-but 2)
      (("17" (skosimp*)
        (("17" (lemma "ext_parallel_pos") (("17" (inst?) nil nil))
          nil))
        nil))
      nil)
     ("18" (hide-all-but 2)
      (("18" (skosimp*)
        (("18" (typepred "y!1`2")
          (("18" (expand "SPP?")
            (("18" (flatten)
              (("18" (split)
                (("1" (expand "PP?")
                  (("1" (prop)
                    (("1" (hide 2) (("1" (grind) nil nil)) nil)
                     ("2" (hide 3) (("2" (grind) nil nil)) nil))
                    nil))
                  nil)
                 ("2" (hide -1)
                  (("2" (expand "SP?")
                    (("2" (skosimp*)
                      (("2" (expand "finseq_appl")
                        (("2" (inst?)
                          (("2" (lemma "ext_preserv_pos")
                            (("2" (inst?) (("2" (grind) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
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      nil)
     ("19" (hide-all-but 2)
      (("19" (skosimp*)
        (("19" (typepred "y!1`2")
          (("19" (expand"SPP?" "SP?")
            (("19" (flatten) (("19" (inst?) nil nil)) nil)) nil))
          nil))
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     ("20" (hide-all-but 1)
      (("20" (skosimp*)
        (("20" (hide-all-but 2)
          (("20" (lemma "ext_parallel_pos") (("20" (inst?) nil nil))
            nil))
          nil))
        nil))
      nil)
     ("21" (hide-all-but 1)
      (("21" (skosimp*)
        (("21" (hide-all-but 2)
          (("21" (typepred "y!1`2")
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                (("21" (split)
                  (("1" (expand "PP?")
                    (("1" (prop)
                      (("1" (hide 2) (("1" (grind) nil nil)) nil)
                       ("2" (hide 3) (("2" (grind) nil nil)) nil))
                      nil))
                    nil)
                   ("2" (hide -1)
                    (("2" (expand "SP?")
                      (("2" (skosimp*)
                        (("2" (expand "finseq_appl")
                          (("2" (inst?)
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                                (inst?)
                                (("2" (grind) nil nil))
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     ("22" (hide-all-but 1)
      (("22" (skosimp*)
        (("22" (typepred "y!1`2")
          (("22" (expand"SPP?" "SP?")
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     ("23" (hide-all-but 2)
      (("23" (skosimp*)
        (("23" (lemma "ext_parallel_pos") (("23" (inst?) nil nil))
          nil))
        nil))
      nil)
     ("24" (hide-all-but 2)
      (("24" (skosimp*)
        (("24" (typepred "fstp!1")
          (("24" (expand "SPP?")
            (("24" (flatten)
              (("24" (split)
                (("1" (expand "PP?")
                  (("1" (prop)
                    (("1" (hide 2) (("1" (grind) nil nil)) nil)
                     ("2" (hide 3) (("2" (grind) nil nil)) nil))
                    nil))
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                 ("2" (hide -1)
                  (("2" (expand "SP?")
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                      (("2" (expand "finseq_appl")
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     ("25" (hide-all-but 2)
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          (("25" (expand"SPP?" "SP?")
            (("25" (flatten) (("25" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((O const-decl "bool" relation_props nil)
    (ext_parallel_pos formula-decl nil substitution nil)
    (i!2 skolem-const-decl "below[length(rest(x!2))]"
     critical_pairs_aux nil)
    (i!1 skolem-const-decl "below[length(x!2)]" critical_pairs_aux nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (length_rest formula-decl nil seq_extras "structures/")
    (preserv_unchanged_subterms formula-decl nil replace_positions nil)
    (subterm_ext_commute formula-decl nil substitution nil)
    (preserv_all_parallel_positions formula-decl nil replace_positions
     nil)
    (ext_preserv_pos formula-decl nil substitution nil)
    (REPtemp skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (replaceTerm def-decl "term" replacement nil)
    (replace_subterm_of_term formula-decl nil replacement nil)
    (RErestTemp skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (i!2 skolem-const-decl
     "below[length(rest[position[variable, symbol, arity]](x!2))]"
     critical_pairs_aux nil)
    (CP_lemma_aux2a1 formula-decl nil replace_positions nil)
    (sg1 skolem-const-decl "Sub[variable, symbol, arity]"
     critical_pairs_aux nil)
    (x!1 skolem-const-decl "term[variable, symbol, arity]"
     critical_pairs_aux nil)
    (x!2 skolem-const-decl "SPP[variable, symbol, arity](x!1)"
     critical_pairs_aux nil)
    (i!2 skolem-const-decl "below[length(rest(x!2))]"
     critical_pairs_aux nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (rest_pos formula-decl nil seq_extras "structures/")
    (rest_parallel_first formula-decl nil substitution nil)
    (seq_first_rest formula-decl nil seq_extras "structures/")
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (first const-decl "T" seq_extras "structures/")
    (SP? const-decl "bool" positions nil)
    (SP type-eq-decl nil positions nil)
    (rest_of_SP_is_SP formula-decl nil positions nil)
    (rest_of_PP_is_PP formula-decl nil positions nil)
    (PP? const-decl "bool" positions nil)
    (PP type-eq-decl nil positions nil)
    (CP_lemma_aux2c1 formula-decl nil critical_pairs_aux nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (nat_min application-judgement "{k: nat | k <= i AND k <= j}"
     real_defs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (^ const-decl "finseq" finite_sequences nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (length_rest_0 formula-decl nil seq_extras "structures/")
    (rest const-decl "finseq" seq_extras "structures/")
    (replace_pos def-decl "term" replace_positions nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (iterate def-decl "pred[[T, T]]" relation_iterate "orders/")
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (positions? type-eq-decl nil positions nil)
    (subtermOF def-decl "term" subterm nil)
    (comp_cont? const-decl "bool" compatibility nil)
    (RSigma const-decl "bool" substitution nil)
    (ext def-decl "term" substitution nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (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)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (positions type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (wf_nat formula-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (naturalnumber type-eq-decl nil naturalnumbers nil)
    (SPP type-eq-decl nil positions nil)
    (SPP? const-decl "bool" positions nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux 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_aux nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (measure_induction formula-decl nil measure_induction nil)
    (well_founded? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil))
   shostak))
 (CP_lemma_aux2d_TCC1 0
  (CP_lemma_aux2d_TCC1-1 nil 3420220323
   ("" (skosimp*)
    (("" (replaces -1)
      (("" (lemma "Pos_var_is_finite")
        (("" (inst?) (("" (assertnil nil)) nil)) nil))
      nil))
    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_is_finite formula-decl nil subterm nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux nil))
   nil))
 (CP_lemma_aux2d_TCC2 0
  (CP_lemma_aux2d_TCC2-1 nil 3420220323
   ("" (skosimp*)
    (("" (rewrite "ext_parallel_pos")
      (("" (hide (-2 -3 2))
        (("" (expand "SPP?")
          (("" (lemma "pos_occ_var_HAStypePP")
            (("" (inst?)
              (("" (assert)
                (("" (lemma "pos_occ_var_HAStypeSP")
                  (("" (inst?) (("" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((ext_parallel_pos formula-decl nil substitution 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)
    (below type-eq-decl nil nat_types nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (position type-eq-decl nil positions nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (SPP? const-decl "bool" positions nil)
    (SPP type-eq-decl nil positions nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (variable formal-nonempty-type-decl nil critical_pairs_aux nil)
    (symbol formal-nonempty-type-decl nil critical_pairs_aux nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (arity formal-const-decl "[symbol -> nat]" critical_pairs_aux nil)
    (pos_occ_var_HAStypeSP formula-decl nil subterm nil)
    (pos_occ_var_HAStypePP formula-decl nil subterm nil))
   nil))
 (CP_lemma_aux2d 0
  (CP_lemma_aux2d-2 nil 3565129732
   ("" (measure-induct+ "card(Pos_var(t,x))" ("t" "x"))
    (("1" (skeep)
      (("1" (name-replace "seqvarsx!2" "set2seq(Pos_var(x!1, x!2))")
        (("1" (expand "replace_pos" 1)
          (("1" (expand "finseq_appl")
            (("1" (lift-if)
              (("1" (prop)
                (("1" (hide -2)
                  (("1" (lemma "same_term")
                    (("1" (inst?)
                      (("1" (assert)
                        (("1" (skeep)
                          (("1" (hide (-3 2))
                            (("1" (expand "RSigma")
                              (("1"
                                (inst -3 "x")
                                (("1"
                                  (prop)
                                  (("1"
                                    (hide (-2 1))
                                    (("1"
                                      (expand "seqvarsx!2")
                                      (("1"
                                        (expand "set2seq")
                                        (("1"
                                          (lift-if)
                                          (("1"
                                            (prop)
                                            (("1" (grind) nil nil)
                                             ("2" (grind) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (case "positionsOF(x!1)(seqvarsx!2`seq(0))")
                  (("1" (lemma "exists_var")
                    (("1" (inst -1 "Vars(x!1)" "Vars(x!1)")
                      (("1" (skosimp*)
                        (("1" (rewrite "union_idempotent")
                          (("1"
                            (inst -2
                             "replaceTerm(x!1, z!1, seqvarsx!2`seq(0))"
                             "x!2")
                            (("1"
                              (inst -2 "R" "gamma(sg1, sg2, x!2, z!1)"
                               "gamma(sg2, sg2, x!2, z!1)")
                              (("1"
                                (prop)
                                (("1"
                                  (name-replace
                                   "seqvarx2Term"
                                   "set2seq(Pos_var(replaceTerm(x!1, z!1, seqvarsx!2`seq(0)), x!2))")
                                  (("1"
                                    (typepred "x!2" "z!1")
                                    (("1"
                                      (expand "V")
                                      (("1"
                                        (expand "ext" -3 2)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand "gamma" -3 2)
                                            (("1"
                                              (expand "ext" 3 (2 3))
                                              (("1"
                                                (lemma
                                                 "ext_replace_ext")
                                                (("1"
                                                  (copy -1)
                                                  (("1"
                                                    (inst?)
                                                    (("1"
                                                      (inst
                                                       -2
                                                       "seqvarsx!2`seq(0)"
                                                       "x!1"
                                                       "gamma(sg2, sg2, x!2, z!1)"
                                                       "z!1")
                                                      (("1"
                                                        (prop)
                                                        (("1"
                                                          (replaces -1)
                                                          (("1"
                                                            (replaces
                                                             -1)
                                                            (("1"
                                                              (expand
                                                               "ext"
                                                               -3
                                                               (2 4))
                                                              (("1"
                                                                (expand
                                                                 "gamma"
                                                                 -3
                                                                 (2 4))
                                                                (("1"
                                                                  (lemma
                                                                   "gamma_term")
                                                                  (("1"
                                                                    (inst?)
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (flatten)
                                                                        (("1"
                                                                          (replace
                                                                           -2
                                                                           -5)
                                                                          (("1"
                                                                            (lemma
                                                                             "replace_subterm_of_term")
                                                                            (("1"
                                                                              (inst
                                                                               -1
                                                                               "seqvarsx!2`seq(0)"
                                                                               "ext(sg2)(x!1)")
                                                                              (("1"
                                                                                (prop)
                                                                                (("1"
                                                                                  (lemma
                                                                                   "subterm_ext_commute")
                                                                                  (("1"
                                                                                    (inst
                                                                                     -1
                                                                                     "seqvarsx!2`seq(0)"
                                                                                     "x!1"
                                                                                     "sg2")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (case-replace
                                                                                         "subtermOF(x!1, seqvarsx!2`seq(0)) = x!2"
                                                                                         :hide?
                                                                                         T)
                                                                                        (("1"
                                                                                          (replaces
                                                                                           -1)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "ext"
                                                                                             -1
                                                                                             2)
                                                                                            (("1"
                                                                                              (replaces
                                                                                               -1)
                                                                                              (("1"
                                                                                                (replace
                                                                                                 -1
                                                                                                 -5)
                                                                                                (("1"
                                                                                                  (lemma
                                                                                                   "CP_lemma_aux2a3")
                                                                                                  (("1"
                                                                                                    (inst
                                                                                                     -1
                                                                                                     "sg2(x!2)"
                                                                                                     "replaceTerm(ext(sg1)(x!1), sg2(x!2), seqvarsx!2`seq(0))"
                                                                                                     "rest(seqvarsx!2)"
                                                                                                     "seqvarx2Term")
                                                                                                    (("1"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide
                                                                                                         (-1
                                                                                                          -2
                                                                                                          -5
                                                                                                          -7
                                                                                                          -8
                                                                                                          4))
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "equivalent")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "finseq_appl")
                                                                                                            (("2"
                                                                                                              (prop)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "seqvarx2Term")
                                                                                                                (("1"
                                                                                                                  (case-replace
                                                                                                                   "rest(seqvarsx!2)`length = seqvarsx!2`length -1"
                                                                                                                   :hide?
                                                                                                                   T)
                                                                                                                  (("1"
                                                                                                                    (lemma
                                                                                                                     "set2seq_length[position]")
                                                                                                                    (("1"
                                                                                                                      (inst?)
                                                                                                                      (("1"
                                                                                                                        (replaces
                                                                                                                         -1)
                                                                                                                        (("1"
                                                                                                                          (lemma
                                                                                                                           "set2seq_length[position]")
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "seqvarsx!2"
                                                                                                                             1
                                                                                                                             1)
                                                                                                                            (("1"
                                                                                                                              (inst?)
                                                                                                                              (("1"
                                                                                                                                (replaces
                                                                                                                                 -1)
                                                                                                                                (("1"
                                                                                                                                  (lemma
                                                                                                                                   "pos_occ_var_replace_as_diff")
                                                                                                                                  (("1"
                                                                                                                                    (inst?)
                                                                                                                                    (("1"
                                                                                                                                      (prop)
                                                                                                                                      (("1"
                                                                                                                                        (replaces
                                                                                                                                         -1)
                                                                                                                                        (("1"
                                                                                                                                          (lemma
                                                                                                                                           "finite_sets[position].card_diff_subset")
                                                                                                                                          (("1"
                                                                                                                                            (inst
                                                                                                                                             -1
                                                                                                                                             "singleton(seqvarsx!2`seq(0))"
                                                                                                                                             "Pos_var(x!1, x!2)")
                                                                                                                                            (("1"
                                                                                                                                              (prop)
                                                                                                                                              (("1"
                                                                                                                                                (rewrite
                                                                                                                                                 "card_singleton")
                                                                                                                                                (("1"
                                                                                                                                                  (expand
                                                                                                                                                   "difference")
                                                                                                                                                  (("1"
                                                                                                                                                    (replace
                                                                                                                                                     -1
                                                                                                                                                     1
                                                                                                                                                     rl)
                                                                                                                                                    (("1"
                                                                                                                                                      (hide
                                                                                                                                                       -1)
                                                                                                                                                      (("1"
                                                                                                                                                        (grind)
                                                                                                                                                        nil
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil)
                                                                                                                                               ("2"
                                                                                                                                                (hide
                                                                                                                                                 2)
                                                                                                                                                (("2"
                                                                                                                                                  (expand*
                                                                                                                                                   "subset?"
                                                                                                                                                   "member")
                                                                                                                                                  (("2"
                                                                                                                                                    (skosimp*)
                                                                                                                                                    (("2"
                                                                                                                                                      (expand
                                                                                                                                                       "singleton")
                                                                                                                                                      (("2"
                                                                                                                                                        (replaces
                                                                                                                                                         -1)
                                                                                                                                                        (("2"
                                                                                                                                                          (lemma
                                                                                                                                                           "set2seq_lem[position]")
                                                                                                                                                          (("2"
                                                                                                                                                            (expand
                                                                                                                                                             "seqvarsx!2"
                                                                                                                                                             (1
                                                                                                                                                              3))
                                                                                                                                                            (("2"
                                                                                                                                                              (inst?)
                                                                                                                                                              (("2"
                                                                                                                                                                (assert)
                                                                                                                                                                (("2"
                                                                                                                                                                  (inst
                                                                                                                                                                   -1
                                                                                                                                                                   "0")
                                                                                                                                                                  (("2"
                                                                                                                                                                    (expand
                                                                                                                                                                     "finseq_appl")
                                                                                                                                                                    (("2"
                                                                                                                                                                      (propax)
                                                                                                                                                                      nil
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil)
                                                                                                                                       ("2"
                                                                                                                                        (hide
                                                                                                                                         2)
                                                                                                                                        (("2"
                                                                                                                                          (lemma
                                                                                                                                           "set2seq_lem[position]")
                                                                                                                                          (("2"
                                                                                                                                            (expand
                                                                                                                                             "seqvarsx!2"
                                                                                                                                             (1
                                                                                                                                              3))
                                                                                                                                            (("2"
                                                                                                                                              (inst?)
                                                                                                                                              (("2"
                                                                                                                                                (assert)
                                                                                                                                                (("2"
                                                                                                                                                  (inst
                                                                                                                                                   -1
                                                                                                                                                   "0")
                                                                                                                                                  (("2"
                                                                                                                                                    (expand
                                                                                                                                                     "finseq_appl")
                                                                                                                                                    (("2"
                                                                                                                                                      (propax)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil)
                                                                                                                                       ("3"
                                                                                                                                        (hide
                                                                                                                                         1)
                                                                                                                                        (("3"
                                                                                                                                          (expand*
                                                                                                                                           "member"
                                                                                                                                           "Vars"
                                                                                                                                           "restrict")
                                                                                                                                          (("3"
                                                                                                                                            (inst
                                                                                                                                             1
                                                                                                                                             "seqvarsx!2`seq(0)")
                                                                                                                                            (("3"
                                                                                                                                              (replaces
                                                                                                                                               -1)
                                                                                                                                              (("3"
                                                                                                                                                (lemma
                                                                                                                                                 "set2seq_lem[position]")
                                                                                                                                                (("3"
                                                                                                                                                  (expand
                                                                                                                                                   "seqvarsx!2")
                                                                                                                                                  (("3"
                                                                                                                                                    (inst?)
                                                                                                                                                    (("3"
                                                                                                                                                      (assert)
                                                                                                                                                      (("3"
                                                                                                                                                        (inst
                                                                                                                                                         -1
                                                                                                                                                         "0")
                                                                                                                                                        (("3"
                                                                                                                                                          (expand
                                                                                                                                                           "finseq_appl")
                                                                                                                                                          (("3"
                                                                                                                                                            (expand
                                                                                                                                                             "Pos_var"
                                                                                                                                                             -1
                                                                                                                                                             1)
                                                                                                                                                            (("3"
                                                                                                                                                              (expand
                                                                                                                                                               "extend"
                                                                                                                                                               -1
                                                                                                                                                               1)
                                                                                                                                                              (("3"
                                                                                                                                                                (propax)
                                                                                                                                                                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
                                                                                                                      4))
                                                                                                                    (("2"
                                                                                                                      (grind)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil)
                                                                                                               ("2"
                                                                                                                (expand
                                                                                                                 "different_elements")
                                                                                                                (("2"
                                                                                                                  (skosimp*)
                                                                                                                  (("2"
                                                                                                                    (expand
                                                                                                                     "finseq_appl")
                                                                                                                    (("2"
                                                                                                                      (lemma
                                                                                                                       "rest_pos[position]")
                                                                                                                      (("2"
                                                                                                                        (inst
                                                                                                                         -1
                                                                                                                         "seqvarsx!2")
                                                                                                                        (("2"
                                                                                                                          (assert)
                                                                                                                          (("2"
                                                                                                                            (lemma
                                                                                                                             "rest_pos[position]")
                                                                                                                            (("2"
                                                                                                                              (inst
                                                                                                                               -1
                                                                                                                               "seqvarsx!2")
                                                                                                                              (("2"
                                                                                                                                (assert)
                                                                                                                                (("2"
                                                                                                                                  (inst
                                                                                                                                   -1
                                                                                                                                   "i!1")
                                                                                                                                  (("1"
                                                                                                                                    (inst
                                                                                                                                     -2
                                                                                                                                     "j!1")
                                                                                                                                    (("1"
                                                                                                                                      (expand
                                                                                                                                       "finseq_appl")
                                                                                                                                      (("1"
                                                                                                                                        (replace
                                                                                                                                         -1
                                                                                                                                         -3
                                                                                                                                         rl)
                                                                                                                                        (("1"
                                                                                                                                          (replace
                                                                                                                                           -2
                                                                                                                                           -3
                                                                                                                                           rl)
                                                                                                                                          (("1"
                                                                                                                                            (hide
                                                                                                                                             (-1
                                                                                                                                              -2))
                                                                                                                                            (("1"
                                                                                                                                              (lemma
                                                                                                                                               "set2seq_neq[position]")
                                                                                                                                              (("1"
                                                                                                                                                (expand
                                                                                                                                                 "seqvarsx!2")
                                                                                                                                                (("1"
                                                                                                                                                  (inst?)
                                                                                                                                                  (("1"
                                                                                                                                                    (assert)
                                                                                                                                                    (("1"
                                                                                                                                                      (inst
                                                                                                                                                       -1
                                                                                                                                                       "1 + i!1"
                                                                                                                                                       "1 + j!1")
                                                                                                                                                      (("1"
                                                                                                                                                        (assert)
                                                                                                                                                        (("1"
                                                                                                                                                          (expand
                                                                                                                                                           "finseq_appl")
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            nil
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil)
                                                                                                                                                       ("2"
                                                                                                                                                        (hide
                                                                                                                                                         (-1
                                                                                                                                                          -4))
                                                                                                                                                        (("2"
                                                                                                                                                          (typepred
                                                                                                                                                           "j!1")
                                                                                                                                                          (("2"
                                                                                                                                                            (expand
                                                                                                                                                             "seqvarsx!2"
                                                                                                                                                             -1)
                                                                                                                                                            (("2"
                                                                                                                                                              (grind)
                                                                                                                                                              nil
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil)
                                                                                                                                                       ("3"
                                                                                                                                                        (hide
                                                                                                                                                         (-1
                                                                                                                                                          -4))
                                                                                                                                                        (("3"
                                                                                                                                                          (typepred
                                                                                                                                                           "i!1")
                                                                                                                                                          (("3"
                                                                                                                                                            (expand
                                                                                                                                                             "seqvarsx!2"
                                                                                                                                                             -1)
                                                                                                                                                            (("3"
                                                                                                                                                              (grind)
                                                                                                                                                              nil
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil)
                                                                                                                                     ("2"
                                                                                                                                      (hide
                                                                                                                                       (-1
                                                                                                                                        -2))
                                                                                                                                      (("2"
                                                                                                                                        (typepred
                                                                                                                                         "j!1")
                                                                                                                                        (("2"
                                                                                                                                          (grind)
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil)
                                                                                                                                   ("2"
                                                                                                                                    (hide
                                                                                                                                     (-1
                                                                                                                                      -2))
                                                                                                                                    (("2"
                                                                                                                                      (typepred
                                                                                                                                       "i!1")
                                                                                                                                      (("2"
                                                                                                                                        (grind)
                                                                                                                                        nil
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil)
                                                                                                               ("3"
                                                                                                                (expand
                                                                                                                 "different_elements")
                                                                                                                (("3"
                                                                                                                  (skosimp*)
                                                                                                                  (("3"
                                                                                                                    (expand
                                                                                                                     "finseq_appl")
                                                                                                                    (("3"
                                                                                                                      (lemma
                                                                                                                       "set2seq_neq[position]")
                                                                                                                      (("3"
                                                                                                                        (expand
                                                                                                                         "seqvarx2Term")
                                                                                                                        (("3"
                                                                                                                          (inst?)
                                                                                                                          (("3"
                                                                                                                            (assert)
                                                                                                                            (("3"
                                                                                                                              (inst
                                                                                                                               -1
                                                                                                                               "i!1"
                                                                                                                               "j!1")
                                                                                                                              (("1"
                                                                                                                                (assert)
                                                                                                                                (("1"
                                                                                                                                  (expand
                                                                                                                                   "finseq_appl")
                                                                                                                                  (("1"
                                                                                                                                    (assert)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("2"
                                                                                                                                (hide
                                                                                                                                 (-1
                                                                                                                                  -4))
                                                                                                                                (("2"
                                                                                                                                  (typepred
                                                                                                                                   "j!1")
                                                                                                                                  (("2"
                                                                                                                                    (expand
                                                                                                                                     "seqvarx2Term")
                                                                                                                                    (("2"
                                                                                                                                      (rewrite
                                                                                                                                       "set2seq_length")
                                                                                                                                      nil
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("3"
                                                                                                                                (hide
                                                                                                                                 (-1
                                                                                                                                  -4))
                                                                                                                                (("3"
                                                                                                                                  (typepred
                                                                                                                                   "i!1")
                                                                                                                                  (("3"
                                                                                                                                    (expand
                                                                                                                                     "seqvarx2Term")
                                                                                                                                    (("3"
                                                                                                                                      (rewrite
                                                                                                                                       "set2seq_length")
                                                                                                                                      nil
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil)
                                                                                                               ("4"
                                                                                                                (skosimp*)
                                                                                                                (("4"
                                                                                                                  (lemma
                                                                                                                   "rest_pos[position]")
                                                                                                                  (("4"
                                                                                                                    (inst?)
                                                                                                                    (("4"
                                                                                                                      (assert)
                                                                                                                      (("4"
                                                                                                                        (inst
                                                                                                                         -1
                                                                                                                         "i!1")
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "finseq_appl")
                                                                                                                          (("1"
                                                                                                                            (replace
                                                                                                                             -1
                                                                                                                             1
                                                                                                                             rl)
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "seqvarsx!2"
                                                                                                                               (1
                                                                                                                                3))
                                                                                                                              (("1"
                                                                                                                                (lemma
                                                                                                                                 "set2seq_lem[position]")
                                                                                                                                (("1"
                                                                                                                                  (inst?)
                                                                                                                                  (("1"
                                                                                                                                    (assert)
                                                                                                                                    (("1"
                                                                                                                                      (inst
                                                                                                                                       -1
                                                                                                                                       "1 + i!1")
                                                                                                                                      (("1"
                                                                                                                                        (expand
                                                                                                                                         "finseq_appl")
                                                                                                                                        (("1"
                                                                                                                                          (expand
                                                                                                                                           "seqvarx2Term")
                                                                                                                                          (("1"
                                                                                                                                            (case
                                                                                                                                             "Pos_var(replaceTerm(x!1, z!1, seqvarsx!2`seq(0)), x!2)(set2seq(Pos_var(x!1, x!2))`seq(1 + i!1))")
                                                                                                                                            (("1"
                                                                                                                                              (lemma
                                                                                                                                               "set2seq_exists[position]")
                                                                                                                                              (("1"
                                                                                                                                                (inst?)
                                                                                                                                                (("1"
                                                                                                                                                  (assert)
                                                                                                                                                  (("1"
                                                                                                                                                    (assert)
                                                                                                                                                    (("1"
                                                                                                                                                      (skosimp*)
                                                                                                                                                      (("1"
                                                                                                                                                        (expand
                                                                                                                                                         "finseq_appl")
                                                                                                                                                        (("1"
                                                                                                                                                          (assert)
                                                                                                                                                          (("1"
                                                                                                                                                            (inst?)
                                                                                                                                                            (("1"
                                                                                                                                                              (assert)
                                                                                                                                                              nil
                                                                                                                                                              nil)
                                                                                                                                                             ("2"
                                                                                                                                                              (typepred
                                                                                                                                                               "ii!1")
                                                                                                                                                              (("2"
                                                                                                                                                                (expand
                                                                                                                                                                 "seqvarx2Term")
                                                                                                                                                                (("2"
                                                                                                                                                                  (propax)
                                                                                                                                                                  nil
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil)
                                                                                                                                                 ("2"
                                                                                                                                                  (hide-all-but
                                                                                                                                                   1)
                                                                                                                                                  (("2"
                                                                                                                                                    (lemma
                                                                                                                                                     "Pos_var_is_finite")
                                                                                                                                                    (("2"
                                                                                                                                                      (inst?)
                                                                                                                                                      (("2"
                                                                                                                                                        (assert)
                                                                                                                                                        nil
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil)
                                                                                                                                             ("2"
                                                                                                                                              (hide
                                                                                                                                               2)
                                                                                                                                              (("2"
                                                                                                                                                (lemma
                                                                                                                                                 "pos_occ_var_replace_as_diff")
                                                                                                                                                (("2"
                                                                                                                                                  (inst?)
                                                                                                                                                  (("2"
                                                                                                                                                    (prop)
                                                                                                                                                    (("1"
                                                                                                                                                      (replaces
                                                                                                                                                       -1)
                                                                                                                                                      (("1"
                                                                                                                                                        (expand
                                                                                                                                                         "difference")
                                                                                                                                                        (("1"
                                                                                                                                                          (expand
                                                                                                                                                           "member")
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            (("1"
                                                                                                                                                              (expand
                                                                                                                                                               "singleton")
                                                                                                                                                              (("1"
                                                                                                                                                                (hide-all-but
                                                                                                                                                                 (-1
                                                                                                                                                                  2))
                                                                                                                                                                (("1"
                                                                                                                                                                  (lemma
                                                                                                                                                                   "set2seq_neq[position]")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (expand
                                                                                                                                                                     "seqvarsx!2")
                                                                                                                                                                    (("1"
                                                                                                                                                                      (inst?)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (assert)
                                                                                                                                                                        (("1"
                                                                                                                                                                          (inst
                                                                                                                                                                           -1
                                                                                                                                                                           "1 + i!1"
                                                                                                                                                                           "0")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (expand
                                                                                                                                                                             "finseq_appl")
                                                                                                                                                                            (("1"
                                                                                                                                                                              (propax)
                                                                                                                                                                              nil
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil)
                                                                                                                                                     ("2"
                                                                                                                                                      (hide-all-but
                                                                                                                                                       (-5
                                                                                                                                                        1
                                                                                                                                                        4))
                                                                                                                                                      (("2"
                                                                                                                                                        (expand
                                                                                                                                                         "seqvarsx!2")
                                                                                                                                                        (("2"
                                                                                                                                                          (lemma
                                                                                                                                                           "set2seq_lem[position]")
                                                                                                                                                          (("2"
                                                                                                                                                            (inst?)
                                                                                                                                                            (("2"
                                                                                                                                                              (assert)
                                                                                                                                                              (("2"
                                                                                                                                                                (inst
                                                                                                                                                                 -1
                                                                                                                                                                 "0")
                                                                                                                                                                (("2"
                                                                                                                                                                  (expand
                                                                                                                                                                   "finseq_appl")
                                                                                                                                                                  (("2"
                                                                                                                                                                    (propax)
                                                                                                                                                                    nil
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil)
                                                                                                                                                     ("3"
                                                                                                                                                      (hide
                                                                                                                                                       (-2
                                                                                                                                                        -3
                                                                                                                                                        1))
                                                                                                                                                      (("3"
                                                                                                                                                        (expand*
                                                                                                                                                         "member"
                                                                                                                                                         "Vars"
                                                                                                                                                         "restrict")
                                                                                                                                                        (("3"
                                                                                                                                                          (inst
                                                                                                                                                           1
                                                                                                                                                           "seqvarsx!2`seq(0)")
                                                                                                                                                          (("3"
                                                                                                                                                            (replaces
                                                                                                                                                             -1)
                                                                                                                                                            (("3"
                                                                                                                                                              (lemma
                                                                                                                                                               "set2seq_lem[position]")
                                                                                                                                                              (("3"
                                                                                                                                                                (expand
                                                                                                                                                                 "seqvarsx!2")
                                                                                                                                                                (("3"
                                                                                                                                                                  (inst?)
                                                                                                                                                                  (("3"
                                                                                                                                                                    (assert)
                                                                                                                                                                    (("3"
                                                                                                                                                                      (inst
                                                                                                                                                                       -1
                                                                                                                                                                       "0")
                                                                                                                                                                      (("3"
                                                                                                                                                                        (expand
                                                                                                                                                                         "finseq_appl")
                                                                                                                                                                        (("3"
                                                                                                                                                                          (expand
                                                                                                                                                                           "Pos_var"
                                                                                                                                                                           -1
                                                                                                                                                                           1)
                                                                                                                                                                          (("3"
                                                                                                                                                                            (expand
                                                                                                                                                                             "extend"
                                                                                                                                                                             -1
                                                                                                                                                                             1)
                                                                                                                                                                            (("3"
                                                                                                                                                                              (propax)
                                                                                                                                                                              nil
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil)
                                                                                                                                       ("2"
                                                                                                                                        (hide
                                                                                                                                         (-1
                                                                                                                                          2))
                                                                                                                                        (("2"
                                                                                                                                          (typepred
                                                                                                                                           "i!1")
                                                                                                                                          (("2"
                                                                                                                                            (expand
                                                                                                                                             "seqvarsx!2")
                                                                                                                                            (("2"
                                                                                                                                              (grind)
                                                                                                                                              nil
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil)
                                                                                                                         ("2"
                                                                                                                          (hide
                                                                                                                           2)
                                                                                                                          (("2"
                                                                                                                            (typepred
                                                                                                                             "i!1")
                                                                                                                            (("2"
                                                                                                                              (grind)
                                                                                                                              nil
                                                                                                                              nil))
                                                                                                                            nil))
--> --------------------

--> maximum size reached

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

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

¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.689Angebot  (Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können 2026-04-27) ¤

*Eine klare Vorstellung vom Zielzustand






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