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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: MPoly.pvs   Sprache: Lisp

Original von: PVS©

(unification
 (IMP_substitution_TCC1 0
  (IMP_substitution_TCC1-1 nil 3463226130
   ("" (lemma "var_countable") (("" (propax) nil nil)) nil)
   ((var_countable formula-decl nil unification nil)) nil))
 (mg_po 0
  (mg_po-1 nil 3455279452
   ("" (expand "preorder?")
    (("" (split)
      (("1" (expand "reflexive?")
        (("1" (skeep)
          (("1" (expand "<=")
            (("1" (inst 1 "identity")
              (("1" (decompose-equality)
                (("1" (expand "comp")
                  (("1" (rewrite "ext_iden"nil nil)) nil))
                nil)
               ("2" (rewrite "iden_subs"nil nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "transitive?")
        (("2" (skeep)
          (("2" (expand "<=")
            (("2" (skosimp*)
              (("2" (inst 1 "comp(tau!2,tau!1)")
                (("1" (replaces -1)
                  (("1" (replaces -1) (("1" (rewrite "o_ass"nil nil))
                    nil))
                  nil)
                 ("2" (rewrite "subs_o"nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((identity const-decl "(bijective?[T, T])" identity nil)
    (bijective? const-decl "bool" functions 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]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (Sub type-eq-decl nil substitution nil)
    (ext_iden formula-decl nil substitution nil)
    (comp const-decl "term" substitution nil)
    (iden_subs formula-decl nil substitution nil)
    (<= const-decl "bool" unification nil)
    (reflexive? const-decl "bool" relations nil)
    (subs_o formula-decl nil substitution nil)
    (o_ass formula-decl nil substitution nil)
    (tau!2 skolem-const-decl "Sub[variable, symbol, arity]" unification
     nil)
    (tau!1 skolem-const-decl "Sub[variable, symbol, arity]" unification
     nil)
    (transitive? const-decl "bool" relations nil)
    (preorder? const-decl "bool" orders nil))
   shostak))
 (uni_diff_equal_length_arg 0
  (uni_diff_equal_length_arg-1 nil 3448191147
   ("" (skosimp*)
    (("" (typepred t!1)
      (("" (expand unifiable)
        (("" (skeep -1)
          (("" (expand unifier)
            (("" (replace -2 -1)
              (("" (replace -3 -1)
                (("" (expand ext)
                  (("" (lift-if)
                    (("" (assert)
                      (("" (decompose-equality -1)
                        (("" (grind) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (unifiable const-decl "bool" unification nil)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (ext def-decl "term" substitution nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (finseq type-eq-decl nil 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) (< const-decl "bool" reals nil)
    (app adt-constructor-decl
     "[[f: symbol, {args: finite_sequence[term] | args`length = arity(f)}] ->
   (app?)]" term_adt nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (unifier const-decl "bool" unification nil))
   shostak))
 (resolving_diff_TCC1 0
  (resolving_diff_TCC1-1 nil 3447690997
   ("" (skosimp*)
    (("" (lemma "positions_of_arg")
      (("" (inst -1 "s!1" "k!1")
        (("1" (typepred "k!1")
          (("1" (lemma "uni_diff_equal_length_arg")
            (("1" (inst -1 "s!1" "t!1" "f!1" "st!1")
              (("1" (assert)
                (("1" (inst -1 "fp!1" "stp!1")
                  (("1" (assert)
                    (("1" (flatten)
                      (("1" (replace -4 1) (("1" (assertnil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assertnil nil))
        nil))
      nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (positions_of_arg formula-decl nil positions nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (uni_diff_equal_length_arg formula-decl nil unification nil)
    (fp!1 skolem-const-decl "symbol" unification nil)
    (stp!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(fp!1)}" unification nil)
    (k!1 skolem-const-decl "below[length(stp!1)]" unification nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (term type-decl nil term_adt nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (resolving_diff_TCC2 0
  (resolving_diff_TCC2-1 nil 3447690997
   ("" (skosimp*)
    (("" (lemma "positions_of_arg")
      (("" (inst -1 "t!1" "k!1")
        (("1" (typepred "k!1")
          (("1" (replace -3 1) (("1" (assertnil nil)) nil)) nil)
         ("2" (assertnil nil))
        nil))
      nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (positions_of_arg formula-decl nil positions nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (fp!1 skolem-const-decl "symbol" unification nil)
    (stp!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(fp!1)}" unification nil)
    (k!1 skolem-const-decl "below[length(stp!1)]" unification nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (t!1 skolem-const-decl "{t: term | unifiable(s!1, t) & s!1 /= t}"
     unification nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (term type-decl nil term_adt nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (resolving_diff_TCC3 0
  (resolving_diff_TCC3-1 nil 3447690997
   ("" (skosimp*)
    (("" (assert)
      (("" (typepred "t!1")
        (("" (expand "unifiable" -1)
          (("" (skeep -1)
            (("" (replace -2 -1)
              (("" (replace -3 -1)
                (("" (expand "unifier" -1)
                  (("" (decompose-equality -1)
                    (("" (assert)
                      (("" (prop)
                        (("1" (hide-all-but (-1 -2 -4 -5))
                          (("1" (expand "ext") (("1" (propax) nil nil))
                            nil))
                          nil)
                         ("2" (expand "ext" -3)
                          (("2" (replace -3 (-2 -4 -6) rl)
                            (("2" (expand "ext" -4)
                              (("2"
                                (flatten)
                                (("2"
                                  (decompose-equality -5)
                                  (("2"
                                    (inst -1 "k!1")
                                    (("1"
                                      (expand "unifiable")
                                      (("1"
                                        (inst 3 "sigma")
                                        (("1" (grind) nil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (expand "unifiable")
                                      (("2"
                                        (inst 4 "sigma")
                                        (("2" (grind) nil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (unifier const-decl "bool" unification nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (< const-decl "bool" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nat_min application-judgement "{k: nat | k <= i AND k <= j}"
     real_defs nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (first const-decl "T" seq_extras "structures/")
    (empty_seq const-decl "finseq" finite_sequences nil)
    (^ const-decl "finseq" finite_sequences nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (subtermOF def-decl "term" subterm nil)
    (st!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(f!1)}" unification nil)
    (f!1 skolem-const-decl "symbol" unification nil)
    (k!1 skolem-const-decl "below[length(stp!1)]" unification nil)
    (stp!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(fp!1)}" unification nil)
    (fp!1 skolem-const-decl "symbol" unification nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (v adt-accessor-decl "[(vars?) -> variable]" term_adt nil)
    (app adt-constructor-decl
     "[[f: symbol, {args: finite_sequence[term] | args`length = arity(f)}] ->
   (app?)]" term_adt nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (ext def-decl "term" substitution 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)
    (vars? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (OR const-decl "[bool, bool -> bool]" booleans 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 unification nil)
    (symbol formal-nonempty-type-decl nil unification 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]" unification nil)
    (term type-decl nil term_adt nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (resolving_diff_TCC4 0
  (resolving_diff_TCC4-1 nil 3449937385
   ("" (skosimp*)
    (("" (expand "<<")
      (("" (lift-if)
        (("" (prop)
          (("1" (hide-all-but (-1 -2)) (("1" (assertnil nil)) nil)
           ("2" (inst 2 k!1)
            (("1" (assert) (("1" (grind) nil nil)) nil)
             ("2" (lemma "uni_diff_equal_length_arg")
              (("2" (inst -1 "s!1" "t!1" "f!1" "st!1")
                (("2" (assert)
                  (("2" (inst -1 "fp!1" "stp!1")
                    (("2" (assert)
                      (("2" (flatten)
                        (("2" (replace -3 1) (("2" (assertnil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((<< adt-def-decl "(strict_well_founded?[term])" term_adt nil)
    (uni_diff_equal_length_arg formula-decl nil unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (unifiable const-decl "bool" unification nil)
    (/= const-decl "boolean" notequal nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" 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)
    (subterm adt-def-decl "boolean" term_adt nil)
    (subtermOF def-decl "term" subterm nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (^ const-decl "finseq" finite_sequences nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (first const-decl "T" seq_extras "structures/")
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (< const-decl "bool" 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)
    (below type-eq-decl nil nat_types nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (symbol formal-nonempty-type-decl nil unification nil)
    (arity formal-const-decl "[symbol -> nat]" unification nil)
    (term type-decl nil term_adt nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (fp!1 skolem-const-decl "symbol" unification nil)
    (stp!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(fp!1)}" unification nil)
    (k!1 skolem-const-decl "below[length(stp!1)]" unification nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   shostak))
 (resolving_diff_TCC5 0
  (resolving_diff_TCC5-1 nil 3449937623
   ("" (skosimp*)
    (("" (lemma "positions_of_arg")
      (("" (inst -1 "s!1" "kk!1")
        (("1" (typepred "kk!1")
          (("1" (lemma "uni_diff_equal_length_arg")
            (("1" (inst -1 "s!1" "t!1" "f!1" "st!1")
              (("1" (assert)
                (("1" (inst -1 "fp!1" "stp!1")
                  (("1" (assert)
                    (("1" (flatten)
                      (("1" (replace -4 1) (("1" (assertnil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assertnil nil))
        nil))
      nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (positions_of_arg formula-decl nil positions nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (uni_diff_equal_length_arg formula-decl nil unification nil)
    (fp!1 skolem-const-decl "symbol" unification nil)
    (stp!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(fp!1)}" unification nil)
    (kk!1 skolem-const-decl "below[length(stp!1)]" unification nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (term type-decl nil term_adt nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   shostak))
 (resolving_diff_TCC6 0
  (resolving_diff_TCC6-1 nil 3516387398
   ("" (skosimp*)
    (("" (lemma "positions_of_arg")
      (("" (inst -1 "t!1" "kk!1")
        (("1" (typepred "kk!1")
          (("1" (replace -3 1) (("1" (assertnil nil)) nil)) nil)
         ("2" (assertnil nil))
        nil))
      nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (positions_of_arg formula-decl nil positions nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (fp!1 skolem-const-decl "symbol" unification nil)
    (stp!1 skolem-const-decl
     "{args: finite_sequence[term[variable, symbol, arity]] |
         args`length = arity(fp!1)}" unification nil)
    (kk!1 skolem-const-decl "below[length(stp!1)]" unification nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (t!1 skolem-const-decl "{t: term | unifiable(s!1, t) & s!1 /= t}"
     unification nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (term type-decl nil term_adt nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (resolving_diff_TCC7 0
  (resolving_diff_TCC7-1 nil 3516387398
   ("" (skosimp*)
    (("" (lemma "uni_diff_equal_length_arg")
      (("" (inst -1 "s!1" "t!1" "f!1" "st!1")
        (("" (assert)
          (("" (inst -1 "fp!1" "stp!1")
            (("" (assert)
              (("" (flatten)
                (("" (replace -1 -4 rl)
                  (("" (hide -1)
                    (("" (typepred t!1)
                      (("" (hide -1)
                        (("" (case "st!1 = stp!1")
                          (("1" (hide +) (("1" (grind) nil nil)) nil)
                           ("2" (decompose-equality 1)
                            (("2" (decompose-equality 1)
                              (("2"
                                (typepred x!1)
                                (("2"
                                  (expand"nonempty?" "empty?")
                                  (("2"
                                    (inst -6 "x!1")
                                    (("2"
                                      (expand "member")
                                      (("2"
                                        (replace -5 -6)
                                        (("2"
                                          (replace -4 -6)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (expand subtermOF)
                                              (("2"
                                                (lift-if)
                                                (("2"
                                                  (assert)
                                                  (("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)
   ((uni_diff_equal_length_arg formula-decl nil unification nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (< const-decl "bool" reals nil) (empty? const-decl "bool" sets nil)
    (nonempty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (subtermOF def-decl "term" subterm nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (first const-decl "T" seq_extras "structures/")
    (empty_seq const-decl "finseq" finite_sequences nil)
    (^ const-decl "finseq" finite_sequences nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nat_min application-judgement "{k: nat | k <= i AND k <= j}"
     real_defs nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" unification 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 unification nil)
    (variable formal-nonempty-type-decl nil unification nil))
   nil))
 (resol_diff_nonempty_implies_funct_terms 0
  (resol_diff_nonempty_implies_funct_terms-1 nil 3450707436
   ("" (skeep)
    (("" (expand "resolving_diff")
      (("" (lift-if)
        (("" (prop) (("1" (assertnil nil) ("2" (assertnil nil))
          nil))
        nil))
      nil))
    nil)
   ((resolving_diff def-decl "position" unification nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   shostak))
 (resol_diff_to_rest_resol_diff_TCC1 0
  (resol_diff_to_rest_resol_diff_TCC1-1 nil 3451131001
   ("" (skeep)
    (("" (lemma "empty_0[posnat]")
      (("" (inst -1 "rd") (("" (assertnil nil)) nil)) nil))
    nil)
   ((posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (empty_0 formula-decl nil seq_extras "structures/")
    (position type-eq-decl nil positions nil)
    (arity formal-const-decl "[symbol -> nat]" unification nil)
    (symbol formal-nonempty-type-decl nil unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   nil))
 (resol_diff_to_rest_resol_diff_TCC2 0
  (resol_diff_to_rest_resol_diff_TCC2-1 nil 3451131001
   ("" (skosimp)
    (("" (expand "resolving_diff" -1)
      (("" (lift-if)
        (("" (prop)
          (("" (assert)
            (("" (replace -1 5)
              (("" (rewrite "first_add")
                (("1" (hide -1 4)
                  (("1" (lemma "resolving_diff_TCC1")
                    (("1" (inst -1 "s!1" "t!1" "f(s!1)" "args(s!1)")
                      (("1" (assert)
                        (("1" (case "s!1 = app( f(s!1), args(s!1))")
                          (("1" (assert)
                            (("1" (inst -2 "f(t!1)" "args(t!1)")
                              (("1"
                                (case "t!1 = app( f(t!1), args(t!1))")
                                (("1"
                                  (assert)
                                  (("1"
                                    (inst
                                     -3
                                     "min({kk: below[length(args(t!1))] |
                                         NOT subtermOF(s!1, #(1 + kk)) = subtermOF(t!1, #(1 + kk))})")
                                    (("1"
                                      (hide 5 2 3 4 5)
                                      (("1"
                                        (lemma "resolving_diff_TCC7")
                                        (("1"
                                          (inst
                                           -1
                                           "s!1"
                                           "t!1"
                                           "f(s!1)"
                                           "args(s!1)")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (inst
                                               -1
                                               "f(t!1)"
                                               "args(t!1)")
                                              (("1" (assertnil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide 2 3 4 5)
                                      (("2"
                                        (skosimp*)
                                        (("2"
                                          (lemma "positions_of_arg")
                                          (("2"
                                            (inst -1 "t!1" "kk!1")
                                            (("2" (assertnil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("3"
                                      (hide 2 3 4 5)
                                      (("3"
                                        (skosimp*)
                                        (("3"
                                          (lemma "positions_of_arg")
                                          (("3"
                                            (inst -1 "s!1" "kk!1")
                                            (("1" (assertnil nil)
                                             ("2"
                                              (typepred "kk!1")
                                              (("2"
                                                (lemma
                                                 "uni_diff_equal_length_arg")
                                                (("2"
                                                  (inst
                                                   -1
                                                   "s!1"
                                                   "t!1"
                                                   "f(s!1)"
                                                   "args(s!1)")
                                                  (("2"
                                                    (assert)
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "f(t!1)"
                                                       "args(t!1)")
                                                      (("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (hide-all-but (1 2))
                                  (("2" (decompose-equality) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide-all-but (1 4))
                            (("2" (decompose-equality) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide -1 5 6)
                  (("2" (lemma "resolving_diff_TCC7")
                    (("2" (inst -1 "s!1" "t!1" "f(s!1)" "args(s!1)")
                      (("2" (assert)
                        (("2" (case "s!1 = app( f(s!1), args(s!1))")
                          (("1" (assert)
                            (("1" (inst -2 "f(t!1)" "args(t!1)")
                              (("1"
                                (case "t!1 = app( f(t!1), args(t!1))")
                                (("1" (assertnil nil)
                                 ("2"
                                  (hide-all-but (1 3))
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                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide-all-but (1 5))
                            (("2" (decompose-equality) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("3" (hide -1 5 6)
                  (("3" (skosimp*)
                    (("3" (lemma "positions_of_arg")
                      (("3" (inst -1 "t!1" "kk!1")
                        (("3" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil)
                 ("4" (hide -1 5 6)
                  (("4" (skosimp*)
                    (("4" (lemma "positions_of_arg")
                      (("4" (inst -1 "s!1" "kk!1")
                        (("1" (assertnil nil)
                         ("2" (typepred "kk!1")
                          (("2" (lemma "uni_diff_equal_length_arg")
                            (("2"
                              (inst -1 "s!1" "t!1" "f(s!1)"
                               "args(s!1)")
                              (("2"
                                (assert)
                                (("2"
                                  (case
                                   "s!1 = app( f(s!1), args(s!1))")
                                  (("1"
                                    (assert)
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                                      (("1"
                                        (assert)
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                                            nil
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                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (hide-all-but (1 6))
                                    (("2"
                                      (decompose-equality)
                                      nil
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((resolving_diff def-decl "position" unification nil)
    (kk!1 skolem-const-decl
     "below[length(args[variable, symbol, arity](t!1))]" unification
     nil)
    (app adt-constructor-decl
     "[[f: symbol, {args: finite_sequence[term] | args`length = arity(f)}] ->
   (app?)]" term_adt nil)
    (term_app_extensionality formula-decl nil term_adt nil)
    (uni_diff_equal_length_arg formula-decl nil unification nil)
    (kk!1 skolem-const-decl
     "below[length(args[variable, symbol, arity](t!1))]" unification
     nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (positions_of_arg formula-decl nil positions nil)
    (resolving_diff_TCC7 subtype-tcc nil unification nil)
    (t!1 skolem-const-decl "{t: term | unifiable(s!1, t) & s!1 /= t}"
     unification nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (resolving_diff_TCC1 subtype-tcc nil unification nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat nil)
    (<= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (< const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (subtermOF def-decl "term" subterm nil)
    (positions? type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions type-eq-decl nil positions nil)
    (position type-eq-decl nil positions nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" unification nil)
    (symbol formal-nonempty-type-decl nil unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (first_add formula-decl nil seq_extras "structures/")
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (resol_diff_to_rest_resol_diff_TCC3 0
  (resol_diff_to_rest_resol_diff_TCC3-1 nil 3451131001
   ("" (skosimp)
    (("" (expand "resolving_diff")
      (("" (lift-if)
        (("" (prop)
          (("" (assert)
            (("" (replace -1 5)
              (("" (rewrite "first_add")
                (("1" (hide -1 4)
                  (("1" (lemma "resolving_diff_TCC2")
                    (("1" (inst -1 "s!1" "t!1" "f(s!1)" "args(s!1)")
                      (("1" (assert)
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                          (("1" (assert)
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                              (("1"
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                                (("1"
                                  (assert)
                                  (("1"
                                    (inst
                                     -3
                                     "min({kk: below[length(args(t!1))] |
                                        NOT subtermOF(s!1, #(1 + kk)) = subtermOF(t!1, #(1 + kk))})")
                                    (("1"
                                      (hide 2 3 4 5)
                                      (("1"
                                        (lemma "resolving_diff_TCC7")
                                        (("1"
                                          (inst
                                           -1
                                           "s!1"
                                           "t!1"
                                           "f(s!1)"
                                           "args(s!1)")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (inst
                                               -1
                                               "f(t!1)"
                                               "args(t!1)")
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                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide 2 3 4 5)
                                      (("2"
                                        (skosimp*)
                                        (("2"
                                          (lemma "positions_of_arg")
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                                            (inst -1 "t!1" "kk!1")
                                            (("2" (assertnil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("3"
                                      (hide 2 3 4 5)
                                      (("3"
                                        (skosimp*)
                                        (("3"
                                          (lemma "positions_of_arg")
                                          (("3"
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                                             ("2"
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                                              (("2"
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                                                 "uni_diff_equal_length_arg")
                                                (("2"
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                                                   -1
                                                   "s!1"
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                                                   "args(s!1)")
                                                  (("2"
                                                    (assert)
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                                                      (inst
                                                       -1
                                                       "f(t!1)"
                                                       "args(t!1)")
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                                                        (assert)
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                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (hide-all-but (1 2))
                                  (("2" (decompose-equality) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide-all-but (1 4))
                            (("2" (decompose-equality) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide -1 5 6)
                  (("2" (lemma "resolving_diff_TCC7")
                    (("2" (inst -1 "s!1" "t!1" "f(s!1)" "args(s!1)")
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                        (("1" (assert)
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                            (("1"
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                              (("1" (assertnil nil)
                               ("2"
                                (hide-all-but (1 3))
                                (("2" (decompose-equality) nil nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide-all-but (1 5))
                          (("2" (decompose-equality) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("3" (hide -1 5 6)
                  (("3" (skosimp*)
                    (("3" (lemma "positions_of_arg")
                      (("3" (inst -1 "t!1" "kk!1")
                        (("3" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil)
                 ("4" (hide -1 5 6)
                  (("4" (skosimp*)
                    (("4" (lemma "positions_of_arg")
                      (("4" (inst -1 "s!1" "kk!1")
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                              (inst -1 "s!1" "t!1" "f(s!1)"
                               "args(s!1)")
                              (("2"
                                (assert)
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                                   "s!1 = app( f(s!1), args(s!1))")
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                                    (assert)
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                                        (assert)
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                                            nil
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                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (hide-all-but (1 6))
                                    (("2"
                                      (decompose-equality)
                                      nil
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((resolving_diff def-decl "position" unification nil)
    (kk!1 skolem-const-decl
     "below[length(args[variable, symbol, arity](t!1))]" unification
     nil)
    (app adt-constructor-decl
     "[[f: symbol, {args: finite_sequence[term] | args`length = arity(f)}] ->
   (app?)]" term_adt nil)
    (term_app_extensionality formula-decl nil term_adt nil)
    (uni_diff_equal_length_arg formula-decl nil unification nil)
    (kk!1 skolem-const-decl
     "below[length(args[variable, symbol, arity](t!1))]" unification
     nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (positions_of_arg formula-decl nil positions nil)
    (resolving_diff_TCC7 subtype-tcc nil unification nil)
    (t!1 skolem-const-decl "{t: term | unifiable(s!1, t) & s!1 /= t}"
     unification nil)
    (s!1 skolem-const-decl "term[variable, symbol, arity]" unification
     nil)
    (resolving_diff_TCC2 subtype-tcc nil unification nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat nil)
    (<= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (args adt-accessor-decl
          "[d: (app?) -> {args: finite_sequence[term] | args`length = arity(f(d))}]"
          term_adt nil)
    (f adt-accessor-decl "[(app?) -> symbol]" term_adt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (app? adt-recognizer-decl "[term -> boolean]" term_adt nil)
    (< const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (|#| const-decl "finite_sequence[T]" set2seq "structures/")
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (subtermOF def-decl "term" subterm nil)
    (positions? type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (positions type-eq-decl nil positions nil)
    (position type-eq-decl nil positions nil)
    (/= const-decl "boolean" notequal nil)
    (unifiable const-decl "bool" unification nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (term type-decl nil term_adt nil)
    (arity formal-const-decl "[symbol -> nat]" unification nil)
    (symbol formal-nonempty-type-decl nil unification nil)
    (variable formal-nonempty-type-decl nil unification nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (first_add formula-decl nil seq_extras "structures/")
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (resol_diff_to_rest_resol_diff_TCC4 0
  (resol_diff_to_rest_resol_diff_TCC4-1 nil 3451131001
   ("" (skosimp)
    (("" (expand "resolving_diff")
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            (("" (reveal 1)
              (("" (assert)
                (("" (hide 5)
                  ((""
                    (name-replace "k1"
                     "min({kk: below[length(args(t!1))]
                              | NOT subtermOF(s!1, #(1 + kk)) = subtermOF(t!1, #(1 + kk))})")
                    (("1" (name-replace "k" "1+k1")
                      (("1" (replace -1 1)
                        (("1" (hide -1)
                          (("1" (rewrite "first_add[posnat]")
                            (("1" (lemma "resolving_diff_TCC3")
                              (("1"
                                (inst
                                 -1
                                 "s!1"
                                 "t!1"
                                 "f(s!1)"
                                 "args(s!1)")
                                (("1"
                                  (case "s!1 = app(f(s!1), args(s!1))")
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                                    (assert)
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                                      (("1"
                                        (case
                                         "t!1 = app(f(t!1), args(t!1))")
                                        (("1"
                                          (assert)
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                                            (inst -3 "k - 1")
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                                              (reveal -6)
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                                                (reveal -5)
                                                (("1"
                                                  (assert)
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                                                nil))
                                              nil)
                                             ("2"
                                              (reveal -6)
                                              (("2"
                                                (reveal -5)
                                                (("2"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide-all-but (1 3))
                                          (("2"
                                            (decompose-equality)
                                            nil
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (hide-all-but (1 5))
                                    (("2"
                                      (decompose-equality)
                                      nil
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.130 Sekunden  (vorverarbeitet)  ¤





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