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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: remoteCounter.mli   Sprache: PVS

Original von: PVS©
(mem_test
 (member_seq_in_seq2set 0
  (member_seq_in_seq2set-1 nil 3569253011
   ("" (skeep) (("" (grind) nil nil)) nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (< 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (below type-eq-decl nil naturalnumbers nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (member_seq const-decl "bool" mem_test nil)
    (T formal-type-decl nil mem_test nil)
    (seq2set const-decl "finite_set[T]" seq2set "structures/"))
   shostak))
 (subseq_rest 0
  (subseq_rest-1 nil 3569226615
   ("" (skeep)
    (("" (expand subseq)
      (("" (skeep)
        (("" (inst -1 i)
          (("" (expand member_seq)
            (("" (expand finseq_appl)
              (("" (skosimp)
                (("" (typepred i!1)
                  (("" (expand rest (-1 -2))
                    (("" (expand* ^ min)
                      (("" (expand empty_seq -1)
                        (("" (lift-if)
                          (("" (assert)
                            (("" (prop) (("" (inst 7 "1+i!1") nil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((subseq const-decl "bool" mem_test 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)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (T formal-type-decl nil mem_test nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (^ const-decl "finseq" finite_sequences nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (member_seq const-decl "bool" mem_test nil))
   shostak))
 (seq2set_comp 0
  (seq2set_comp-1 nil 3569231569
   ("" (skeep)
    (("" (split)
      (("1" (flatten)
        (("1" (expand o)
          (("1" (expand seq2set)
            (("1" (expand finseq_appl)
              (("1" (skosimp)
                (("1" (lift-if)
                  (("1" (prop)
                    (("1" (inst 1 kk!1) nil nil)
                     ("2" (inst 3 "kk!1 - seq1`length")
                      (("2" (assert) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (flatten)
        (("2" (expand o)
          (("2" (expand seq2set)
            (("2" (expand finseq_appl)
              (("2" (split)
                (("1" (skosimp)
                  (("1" (inst 1 kk!1)
                    (("1" (lift-if) (("1" (assert) nil nil)) nil)
                     ("2" (assert) nil nil))
                    nil))
                  nil)
                 ("2" (skosimp)
                  (("2" (inst 1 "kk!1+seq1`length")
                    (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((O const-decl "finseq" finite_sequences nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (kk!1 skolem-const-decl "below(seq1`length + seq2`length)" mem_test
     nil)
    (seq2 skolem-const-decl "finseq[T]" mem_test nil)
    (seq1 skolem-const-decl "finseq[T]" mem_test nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (T formal-type-decl nil mem_test nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil naturalnumbers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (seq2set const-decl "finite_set[T]" seq2set "structures/")
    (kk!1 skolem-const-decl "below(length(seq1))" mem_test nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil))
   shostak))
 (seq_construct_TCC1 0
  (seq_construct_TCC1-1 nil 3575042025 ("" (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)
    (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)
    (>= 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil))
   nil))
 (seq_construct_TCC2 0
  (seq_construct_TCC2-1 nil 3575042025 ("" (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)
    (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)
    (>= 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (< const-decl "bool" reals nil))
   nil))
 (seq_construct_TCC3 0
  (seq_construct_TCC3-1 nil 3575042025 ("" (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)
    (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)
    (>= 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil))
   nil))
 (seq_construct_TCC4 0
  (seq_construct_TCC4-1 nil 3575042025 ("" (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)
    (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)
    (>= 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil))
   nil))
 (seq_construct_TCC5 0
  (seq_construct_TCC5-1 nil 3575042025 ("" (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)
    (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)
    (>= 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil))
   nil))
 (seq_construct 0
  (seq_construct-1 nil 3575042028
   ("" (induct n)
    (("1" (skeep)
      (("1" (inst 1 empty_seq)
        (("1" (expand empty_seq 1 1) (("1" (skeep) nil nil)) nil))
        nil))
      nil)
     ("2" (skeep)
      (("2" (skeep)
        (("2" (inst -1 P "rest(seq1)" "rest(seq2)")
          (("2" (prop)
            (("1" (inst -4 0)
              (("1" (skosimp*)
                (("1" (inst 1 "add_first(x!1, seq!1)")
                  (("1" (expand* add_first insert? finseq_appl)
                    (("1" (assert)
                      (("1" (skeep)
                        (("1" (lift-if)
                          (("1" (case "i=0")
                            (("1" (assert) nil nil)
                             ("2" (assert)
                              (("2"
                                (inst -2 i-1)
                                (("2"
                                  (expand rest -2)
                                  (("2"
                                    (expand* ^ min empty_seq)
                                    nil
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (hide-all-but (-1 1)) (("2" (grind) nil nil)) nil)
             ("3" (hide-all-but (-2 1)) (("3" (grind) nil nil)) nil)
             ("4" (hide 2)
              (("4" (skeep)
                (("4" (typepred i)
                  (("4" (expand* rest ^ min empty_seq)
                    (("4" (assert) (("4" (inst -4 1+i) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2)
      (("3" (skeep)
        (("3" (skeep) (("3" (skeep) (("3" (assert) nil nil)) nil))
          nil))
        nil))
      nil)
     ("4" (hide 2)
      (("4" (skeep)
        (("4" (skeep) (("4" (skeep) (("4" (assert) nil nil)) nil))
          nil))
        nil))
      nil)
     ("5" (hide 2)
      (("5" (skeep) (("5" (skeep) (("5" (assert) nil nil)) nil)) nil))
      nil)
     ("6" (hide 2)
      (("6" (skeep) (("6" (skeep) (("6" (assert) nil nil)) nil)) nil))
      nil)
     ("7" (hide 2) (("7" (skeep) (("7" (assert) nil nil)) nil)) nil)
     ("8" (hide 2) (("8" (skeep) (("8" (assert) nil nil)) nil)) nil))
    nil)
   ((rest const-decl "finseq" seq_extras "structures/")
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (add_first const-decl "finseq" seq_extras "structures/")
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (^ const-decl "finseq" finite_sequences nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (insert? const-decl "finseq" seq_extras "structures/")
    (empty_seq const-decl "finseq" finite_sequences nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (pred type-eq-decl nil defined_types 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)
    (below type-eq-decl nil nat_types nil)
    (T formal-type-decl nil mem_test nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (< const-decl "bool" reals nil))
   shostak))
 (seq_construct2_TCC1 0
  (seq_construct2_TCC1-1 nil 3575131546 ("" (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)
    (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)
    (>= 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil))
   nil))
 (seq_construct2 0
  (seq_construct2-1 nil 3575131579
   ("" (induct n)
    (("1" (skeep)
      (("1" (inst 1 empty_seq)
        (("1" (expand empty_seq 1 1) (("1" (skeep) nil nil)) nil))
        nil))
      nil)
     ("2" (skeep)
      (("2" (skeep)
        (("2" (inst -1 P1)
          (("2" (prop)
            (("1" (skosimp)
              (("1" (inst -3 j)
                (("1" (skosimp)
                  (("1" (inst 1 "add_last(seq!1, x!1)")
                    (("1" (expand* add_last insert? finseq_appl)
                      (("1" (assert)
                        (("1" (skeep)
                          (("1" (lift-if)
                            (("1" (prop)
                              (("1"
                                (inst -3 i)
                                (("1" (assert) nil nil))
                                nil)
                               ("2"
                                (typepred i)
                                (("2" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (hide 2)
              (("2" (skeep) (("2" (inst -1 i) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2)
      (("3" (skeep) (("3" (skeep) (("3" (assert) nil nil)) nil)) nil))
      nil))
    nil)
   ((insert? const-decl "finseq" seq_extras "structures/")
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (i skolem-const-decl "below[1 + j]" mem_test nil)
    (j skolem-const-decl "nat" mem_test nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (add_last const-decl "finseq" seq_extras "structures/")
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types 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)
    (T formal-type-decl nil mem_test nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (= const-decl "[T, T -> boolean]" equalities nil))
   shostak)))
(orthogonality
 (IMP_critical_pairs_TCC1 0
  (IMP_critical_pairs_TCC1-1 nil 3581385367
   ("" (rewrite "var_countable") nil nil)
   ((var_countable formula-decl nil orthogonality nil)) nil))
 (ntCP?_TCC1 0
  (ntCP?_TCC1-1 nil 3581173294
   ("" (skosimp*)
    (("" (hide-all-but 3)
      (("" (typepred "p!1") (("" (rewrite "ext_preserv_pos") nil nil))
        nil))
      nil))
    nil)
   ((ext_preserv_pos formula-decl nil substitution nil)
    (V const-decl "set[term]" variables_term nil)
    (Sub? const-decl "bool" substitution nil)
    (Sub type-eq-decl nil substitution nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (variable formal-nonempty-type-decl nil orthogonality nil)
    (symbol formal-nonempty-type-decl nil orthogonality 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]" orthogonality nil)
    (term type-decl nil term_adt 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)
    (positions type-eq-decl nil positions nil)
    (positionsOF def-decl "positions" positions nil)
    (rewrite_rule? const-decl "bool" rewrite_rules nil)
    (rewrite_rule type-eq-decl nil rewrite_rules nil)
    (lhs const-decl "term" rewrite_rules nil)
    (set type-eq-decl nil sets nil) (member const-decl "bool" sets nil)
    (positions? type-eq-decl nil positions nil))
   nil))
 (ntCP_lemma_aux1_TCC1 0
  (ntCP_lemma_aux1_TCC1-1 nil 3581173294
   ("" (skosimp*)
    (("" (hide-all-but (-1 3))
      (("" (rewrite "ext_preserv_pos") nil nil)) nil))
    nil)
   ((arity formal-const-decl "[symbol -> nat]" orthogonality 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 orthogonality nil)
    (variable formal-nonempty-type-decl nil orthogonality nil)
    (Sub type-eq-decl nil substitution nil)
    (Sub? const-decl "bool" substitution nil)
    (V const-decl "set[term]" variables_term nil)
    (member const-decl "bool" sets nil) (set type-eq-decl nil sets nil)
    (lhs const-decl "term" rewrite_rules nil)
    (rewrite_rule type-eq-decl nil rewrite_rules nil)
    (rewrite_rule? const-decl "bool" rewrite_rules nil)
    (term type-decl nil term_adt nil)
    (position type-eq-decl nil positions nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil nat_types nil)
    (ext_preserv_pos formula-decl nil substitution nil))
   nil))
 (ntCP_lemma_aux1 0
  (ntCP_lemma_aux1-1 nil 3581173357
   ("" (skosimp*)
    (("" (lemma "CP_lemma_aux1a")
      (("" (inst?)
        (("" (assert)
          (("" (skosimp*)
            ((""
              (case "ext(union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))))(subtermOF(lhs(e1!1), p!1)) = ext(union_subs((restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))))(ext(rho!1)(lhs(e2!1)))")
              (("1" (lemma "unification")
                (("1"
                  (inst -1 "subtermOF(lhs(e1!1), p!1)"
                   "ext(rho!1)(lhs(e2!1))")
                  (("1" (hide 2)
                    (("1" (prop)
                      (("1" (skosimp*)
                        (("1" (copy -1)
                          (("1" (expand "mgu" -1)
                            (("1" (flatten)
                              (("1"
                                (hide -1)
                                (("1"
                                  (inst
                                   -1
                                   "union_subs(restriction(sg1!1)(Vars(lhs(e1!1))), restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                  (("1"
                                    (expand "member" -1)
                                    (("1"
                                      (expand "U" -1)
                                      (("1"
                                        (expand "unifier" -1)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand "<=")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (inst
                                                 2
                                                 "ext(theta!1)(rhs(e1!1))"
                                                 "replaceTerm(ext(theta!1)(lhs(e1!1)), ext(theta!1)(ext(rho!1)(rhs(e2!1))),p!1)"
                                                 "tau!1")
                                                (("1"
                                                  (lemma "ext_o")
                                                  (("1"
                                                    (inst
                                                     -1
                                                     "tau!1"
                                                     "theta!1")
                                                    (("1"
                                                      (decompose-equality
                                                       -1)
                                                      (("1"
                                                        (split)
                                                        (("1"
                                                          (hide -1)
                                                          (("1"
                                                            (expand
                                                             "ntCP?")
                                                            (("1"
                                                              (inst
                                                               1
                                                               "theta!1"
                                                               "rho!1"
                                                               "e1!1"
                                                               "e2!1"
                                                               "p!1")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (reveal
                                                                   3)
                                                                  (("1"
                                                                    (propax)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("2"
                                                          (inst
                                                           -1
                                                           "rhs(e1!1)")
                                                          (("2"
                                                            (expand
                                                             "o")
                                                            (("2"
                                                              (replace
                                                               -1
                                                               1
                                                               rl)
                                                              (("2"
                                                                (hide
                                                                 -1)
                                                                (("2"
                                                                  (replace
                                                                   -1
                                                                   1
                                                                   rl)
                                                                  (("2"
                                                                    (hide
                                                                     -1)
                                                                    (("2"
                                                                      (lemma
                                                                       "restriction_union")
                                                                      (("2"
                                                                        (inst
                                                                         -1
                                                                         "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                                                         "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                                                         "rhs(e1!1)")
                                                                        (("1"
                                                                          (lemma
                                                                           "dom_restriction")
                                                                          (("1"
                                                                            (copy
                                                                             -1)
                                                                            (("1"
                                                                              (inst
                                                                               -1
                                                                               "Vars(lhs(e1!1))"
                                                                               "sg1!1")
                                                                              (("1"
                                                                                (inst
                                                                                 -2
                                                                                 "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                 "alpha!1")
                                                                                (("1"
                                                                                  (lemma
                                                                                   "IUnion_extra[(V)].disjoint_subset")
                                                                                  (("1"
                                                                                    (inst
                                                                                     -1
                                                                                     "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                     "Vars(lhs(e1!1))"
                                                                                     "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                     "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (prop)
                                                                                        (("1"
                                                                                          (replace
                                                                                           -1
                                                                                           1)
                                                                                          (("1"
                                                                                            (lemma
                                                                                             "restriction_term")
                                                                                            (("1"
                                                                                              (inst?)
                                                                                              (("1"
                                                                                                (prop)
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (hide-all-but
                                                                                                   1)
                                                                                                  (("2"
                                                                                                    (typepred
                                                                                                     "e1!1")
                                                                                                    (("2"
                                                                                                      (expand
                                                                                                       "rewrite_rule?")
                                                                                                      (("2"
                                                                                                        (expand*
                                                                                                         "lhs"
                                                                                                         "rhs")
                                                                                                        (("2"
                                                                                                          (prop)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            -6
                                                                                            1))
                                                                                          (("2"
                                                                                            (lemma
                                                                                             "IUnion_extra[(V)].disjoint_subset")
                                                                                            (("2"
                                                                                              (inst
                                                                                               -1
                                                                                               "Vars(rhs(e1!1))"
                                                                                               "Vars(rhs(e1!1))"
                                                                                               "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                               "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                              (("2"
                                                                                                (prop)
                                                                                                (("1"
                                                                                                  (hide-all-but
                                                                                                   1)
                                                                                                  (("1"
                                                                                                    (expand*
                                                                                                     "subset?"
                                                                                                     "member")
                                                                                                    (("1"
                                                                                                      (skeep)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (hide-all-but
                                                                                                   (-3
                                                                                                    1))
                                                                                                  (("2"
                                                                                                    (lemma
                                                                                                     "IUnion_extra[(V)].disjoint_subset")
                                                                                                    (("2"
                                                                                                      (inst
                                                                                                       -1
                                                                                                       "Vars(rhs(e1!1))"
                                                                                                       "Vars(lhs(e1!1))"
                                                                                                       "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                                       "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                                      (("2"
                                                                                                        (prop)
                                                                                                        (("1"
                                                                                                          (hide
                                                                                                           (-1
                                                                                                            2))
                                                                                                          (("1"
                                                                                                            (typepred
                                                                                                             "e1!1")
                                                                                                            (("1"
                                                                                                              (expand*
                                                                                                               "rewrite_rule?"
                                                                                                               "lhs"
                                                                                                               "rhs")
                                                                                                              (("1"
                                                                                                                (assert)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (hide
                                                                                                           (-1
                                                                                                            2))
                                                                                                          (("2"
                                                                                                            (expand*
                                                                                                             "subset?"
                                                                                                             "member")
                                                                                                            (("2"
                                                                                                              (skeep)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (rewrite
                                                                           "restriction_Subs")
                                                                          nil
                                                                          nil)
                                                                         ("3"
                                                                          (rewrite
                                                                           "restriction_Subs")
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("3"
                                                          (lemma
                                                           "ext_replace_ext")
                                                          (("3"
                                                            (inst?)
                                                            (("3"
                                                              (prop)
                                                              (("1"
                                                                (replaces
                                                                 -1)
                                                                (("1"
                                                                  (copy
                                                                   -1)
                                                                  (("1"
                                                                    (inst
                                                                     -1
                                                                     "ext(rho!1)(rhs(e2!1))")
                                                                    (("1"
                                                                      (inst
                                                                       -2
                                                                       "lhs(e1!1)")
                                                                      (("1"
                                                                        (expand
                                                                         "o")
                                                                        (("1"
                                                                          (replace
                                                                           -1
                                                                           1
                                                                           rl)
                                                                          (("1"
                                                                            (replace
                                                                             -2
                                                                             1
                                                                             rl)
                                                                            (("1"
                                                                              (replace
                                                                               -3
                                                                               1
                                                                               rl)
                                                                              (("1"
                                                                                (hide
                                                                                 (-1
                                                                                  -2
                                                                                  -3))
                                                                                (("1"
                                                                                  (lemma
                                                                                   "restriction_union")
                                                                                  (("1"
                                                                                    (copy
                                                                                     -1)
                                                                                    (("1"
                                                                                      (inst
                                                                                       -1
                                                                                       "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                                                                       "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                                                                       "lhs(e1!1)")
                                                                                      (("1"
                                                                                        (inst
                                                                                         -2
                                                                                         "restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1))))"
                                                                                         "restriction(sg1!1)(Vars(lhs(e1!1)))"
                                                                                         "ext(rho!1)(rhs(e2!1))")
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "dom_restriction")
                                                                                          (("1"
                                                                                            (copy
                                                                                             -1)
                                                                                            (("1"
                                                                                              (inst
                                                                                               -1
                                                                                               "Vars(lhs(e1!1))"
                                                                                               "sg1!1")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -2
                                                                                                 "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                                 "alpha!1")
                                                                                                (("1"
                                                                                                  (lemma
                                                                                                   "IUnion_extra[(V)].disjoint_subset")
                                                                                                  (("1"
                                                                                                    (inst
                                                                                                     -1
                                                                                                     "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                     "Vars(lhs(e1!1))"
                                                                                                     "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))"
                                                                                                     "Vars(ext(rho!1)(lhs(e2!1)))")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (lemma
                                                                                                         "IUnion_extra[(V)].disjoint_commute")
                                                                                                        (("1"
                                                                                                          (inst
                                                                                                           -1
                                                                                                           "Dom(restriction(sg1!1)(Vars(lhs(e1!1))))"
                                                                                                           "Dom(restriction(alpha!1)(Vars(ext(rho!1)(lhs(e2!1)))))")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            (("1"
                                                                                                              (prop)
                                                                                                              (("1"
                                                                                                                (rewrite
                                                                                                                 "union_commute")
                                                                                                                (("1"
                                                                                                                  (replaces
                                                                                                                   -1)
                                                                                                                  (("1"
                                                                                                                    (replaces
                                                                                                                     -1)
                                                                                                                    (("1"
                                                                                                                      (lemma
                                                                                                                       "restriction_term")
                                                                                                                      (("1"
                                                                                                                        (copy
                                                                                                                         -1)
                                                                                                                        (("1"
                                                                                                                          (inst
                                                                                                                           -1
                                                                                                                           "Vars(ext(rho!1)(lhs(e2!1)))"
                                                                                                                           "alpha!1"
                                                                                                                           "ext(rho!1)(rhs(e2!1))")
                                                                                                                          (("1"
                                                                                                                            (inst
                                                                                                                             -2
                                                                                                                             "Vars(lhs(e1!1))"
                                                                                                                             "sg1!1"
                                                                                                                             "lhs(e1!1)")
                                                                                                                            (("1"
                                                                                                                              (prop)
                                                                                                                              (("1"
                                                                                                                                (replace
                                                                                                                                 -1
                                                                                                                                 1
--> --------------------

--> maximum size reached

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