SSL csequence_append.prf Sprache: Lisp

(csequence_append
(append_struct_TCC1 0
  (append_struct_TCC1-1 nil 3513600229 ("" (subtype-tcc) nil nil) nil
   nil))
(append_TCC1 0
  (append_TCC1-1 nil 3513600229
   ("" (expand* "append_struct" "coreduce") (("" (reduce) nil nil))
    nil)
   ((append_struct const-decl "csequence_struct" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil))
   nil))
(append_finite 0
  (append_finite-1 nil 3513600229
   ("" (induct "fseq" :name "is_finite_induction")
    (("1" (skolem!) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)
     ("2" (assert) nil nil) ("3" (assert) nil nil)
     ("4" (skosimp*)
      (("4" (expand "is_finite" +)
        (("4" (expand* "append" "append_struct")
          (("4" (expand "coreduce" +) (("4" (reduce) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((append_struct const-decl "csequence_struct" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_append nil)
    (append const-decl "nonempty_csequence" csequence_append nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil))
   nil))
(append_first_TCC1 0
  (append_first_TCC1-1 nil 3513600229 ("" (subtype-tcc) nil nil) nil
   nil))
(append_first 0
  (append_first-1 nil 3513600683
   ("" (expand* "append" "append_struct" "coreduce")
    (("" (reduce) nil nil)) nil)
   ((append const-decl "nonempty_csequence" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (append_struct const-decl "csequence_struct" csequence_append nil))
   shostak))
(append_rest 0
  (append_rest-1 nil 3513600699
   ("" (skolem!)
    (("" (lemma "coinduction")
      ((""
        (inst -
         "LAMBDA (cseq1, cseq2: csequence): (empty?(cseq1) AND empty?(cseq2)) OR (EXISTS nseq: cseq1 = append(t!1, rest(nseq)) AND cseq2 = rest(append(t!1, nseq)))"
         "append(t!1, rest(nseq!1))" "rest(append(t!1, nseq!1))")
        (("1" (assert) (("1" (inst?) nil nil)) nil)
         ("2" (delete 2)
          (("2" (expand "bisimulation?")
            (("2" (skosimp* t)
              (("2" (smash)
                (("1" (grind) nil nil)
                 ("2" (skosimp)
                  (("2" (inst + "rest(nseq!2)")
                    (("1" (expand* "append" "append_struct" "coreduce")
                      (("1" (grind) nil nil)) nil)
                     ("2" (grind) nil nil))
                    nil))
                  nil)
                 ("3" (skosimp)
                  (("3" (inst + "rest(nseq!2)")
                    (("1" (expand* "append" "append_struct" "coreduce")
                      (("1" (grind) nil nil)) nil)
                     ("2" (grind) nil nil))
                    nil))
                  nil)
                 ("4" (grind) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil csequence_append nil)
    (coinduction formula-decl nil csequence_codt nil)
    (nseq!2 skolem-const-decl "nonempty_csequence[T]" csequence_append
     nil)
    (nseq!2 skolem-const-decl "nonempty_csequence[T]" csequence_append
     nil)
    (append_struct const-decl "csequence_struct" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (csequence type-decl nil csequence_codt nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (PRED type-eq-decl nil defined_types nil)
    (bisimulation? adt-def-decl "boolean" csequence_codt nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
     nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (append const-decl "nonempty_csequence" csequence_append nil)
    (t!1 skolem-const-decl "T" csequence_append nil)
    (rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
          nil))
   shostak))
(append_finite_def 0
  (append_finite_def-1 nil 3513600841
   ("" (induct "fseq" :name "is_finite_induction")
    (("1" (assert) nil nil) ("2" (assert) nil nil)
     ("3" (skosimp*)
      (("3" (use "length_empty?_rew")
        (("3" (reduce)
          (("1"
            (expand* "insert" "append" "append_struct" "coreduce"
             "coreduce")
            (("1" (assert) nil nil)) nil)
           ("2" (decompose-equality 3)
            (("1" (rewrite "append_first")
              (("1" (rewrite "insert_first") nil nil)) nil)
             ("2" (rewrite "append_rest")
              (("2" (rewrite "insert_rest")
                (("2" (expand "length" 1) (("2" (propax) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((append_struct const-decl "csequence_struct" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (append_rest formula-decl nil csequence_append nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (insert_rest formula-decl nil csequence_insert nil)
    (append_first formula-decl nil csequence_append nil)
    (insert_first formula-decl nil csequence_insert nil)
    (csequence_add_extensionality formula-decl nil csequence_codt nil)
    (length_empty?_rew formula-decl nil csequence_length nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_append nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (has_length def-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (insert def-decl "nonempty_csequence" csequence_insert 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)
    (append const-decl "nonempty_csequence" csequence_append nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil))
   shostak))
(append_infinite_def 0
  (append_infinite_def-1 nil 3513601029
   ("" (skolem!)
    (("" (lemma "coinduction")
      ((""
        (inst -
         "LAMBDA (cseq1, cseq2: csequence): is_infinite(cseq2) AND cseq1 = append(t!1, cseq2)"
         "append(t!1, iseq!1)" "iseq!1")
        (("1" (assert) nil nil)
         ("2" (delete 2)
          (("2" (expand "bisimulation?")
            (("2" (skosimp)
              (("2" (expand "is_finite" 1)
                (("2" (grind :rewrites ("append_rest")) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil csequence_append nil)
    (coinduction formula-decl nil csequence_codt nil)
    (append_struct const-decl "csequence_struct" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (csequence type-decl nil csequence_codt nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (PRED type-eq-decl nil defined_types nil)
    (bisimulation? adt-def-decl "boolean" csequence_codt nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (append const-decl "nonempty_csequence" csequence_append nil)
    (t!1 skolem-const-decl "T" csequence_append nil))
   shostak))
(append_length 0
  (append_length-1 nil 3513601102
   ("" (induct "fseq" :name "is_finite_induction")
    (("1" (assert) nil nil) ("2" (assert) nil nil)
     ("3" (skosimp*)
      (("3" (expand "length" +)
        (("3" (reduce)
          (("1"
            (expand* "append" "append_struct" "coreduce" "coreduce"
             "length")
            nil nil)
           ("2"
            (expand* "append" "append_struct" "coreduce" "coreduce"
             "length")
            nil nil)
           ("3" (rewrite "append_rest") nil nil))
          nil))
        nil))
      nil)
     ("4" (skosimp*)
      (("4" (use "append_finite" ("fseq" "fseq!2")) nil nil)) nil))
    nil)
   ((append_finite judgement-tcc nil csequence_append nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (even_plus_odd_is_odd application-judgement "odd_int" integers nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (append_struct const-decl "csequence_struct" csequence_append nil)
    (append_rest formula-decl nil csequence_append nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (T formal-type-decl nil csequence_append nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (has_length def-decl "bool" csequence_props 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)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number nonempty-type-decl nil numbers nil)
    (csequence type-decl nil csequence_codt nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (append const-decl "nonempty_csequence" csequence_append nil))
   shostak))
(append_index 0
  (append_index-1 nil 3513601245
   ("" (induct "n")
    (("1" (skolem!)
      (("1" (use "length_empty?_rew")
        (("1" (expand "index?") (("1" (ground) nil nil)) nil)) nil))
      nil)
     ("2" (skosimp*)
      (("2" (case "empty?(cseq!1)")
        (("1" (hide -2)
          (("1" (use "length_empty?_rew")
            (("1"
              (expand* "append" "append_struct" "coreduce" "coreduce"
               "index?" "index?")
              (("1" (ground) nil nil)) nil))
            nil))
          nil)
         ("2" (assert)
          (("2" (inst - "t!1" "rest(cseq!1)")
            (("2" (auto-rewrite "index?_prop")
              (("2" (assert)
                (("2" (expand* "append" "append_struct")
                  (("2" (expand "coreduce" +)
                    (("2" (expand "is_finite" +)
                      (("2" (expand "length" +)
                        (("2" (reduce) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((index?_prop formula-decl nil csequence_nth nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
          nil)
    (append_struct const-decl "csequence_struct" csequence_append nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
     nil)
    (length_empty?_rew formula-decl nil csequence_length nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (has_length def-decl "bool" csequence_props nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (append const-decl "nonempty_csequence" csequence_append nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (index? def-decl "bool" csequence_nth nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_append nil)
    (pred type-eq-decl nil defined_types 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))
   shostak))
(append_nth_TCC1 0
  (append_nth_TCC1-1 nil 3513600229
   ("" (skolem!) (("" (rewrite "append_index") nil nil)) nil)
   ((append_index formula-decl nil csequence_append nil)
    (T formal-type-decl nil csequence_append nil)
    (csequence type-decl nil csequence_codt 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)
    (index? def-decl "bool" csequence_nth nil)
    (indexes type-eq-decl nil csequence_nth nil))
   nil))
(append_nth 0
  (append_nth-1 nil 3513601432
   ("" (skolem-typepred)
    (("" (rewrite "index?_prop")
      (("" (split)
        (("1" (rewrite "append_finite_def")
          (("1" (use "insert_nth")
            (("1" (lift-if) (("1" (assert) nil nil)) nil)) nil))
          nil)
         ("2" (rewrite "append_infinite_def") nil nil))
        nil))
      nil))
    nil)
   ((index?_prop formula-decl nil csequence_nth nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (append_infinite_def formula-decl nil csequence_append nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (append_finite_def formula-decl nil csequence_append nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (has_length def-decl "bool" csequence_props nil)
    (insert_nth formula-decl nil csequence_insert nil)
    (indexes type-eq-decl nil csequence_nth nil)
    (index? def-decl "bool" csequence_nth 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)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_append nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   shostak))
(append_add 0
  (append_add-1 nil 3513601483
   ("" (expand* "append" "append_struct" "coreduce")
    (("" (expand "coreduce" 1 2) (("" (propax) nil nil)) nil)) nil)
   ((append const-decl "nonempty_csequence" csequence_append nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (append_struct const-decl "csequence_struct" csequence_append nil))
   shostak))
(append_last 0
  (append_last-1 nil 3513601569
   ("" (skolem + ("t!1" "_"))
    (("" (induct "fseq" :name "is_finite_induction")
      (("1" (assert) nil nil) ("2" (assert) nil nil)
       ("3" (skosimp)
        (("3" (ground)
          (("1"
            (expand* "append" "append_struct" "coreduce" "coreduce"
             "last" "length" "length" "nth")
            nil nil)
           ("2" (lemma "last_rest" ("nfseq" "append(t!1, cseq!1)"))
            (("2" (rewrite "append_rest") (("2" (assert) nil nil))
              nil))
            nil))
          nil))
        nil)
       ("4" (skosimp)
        (("4" (use "append_finite" ("fseq" "fseq!2")) nil nil)) nil))
      nil))
    nil)
   ((t!1 skolem-const-decl "T" csequence_append nil)
    (append const-decl "nonempty_csequence" csequence_append nil)
    (nonempty_csequence type-eq-decl nil csequence_props nil)
    (nonempty? adt-recognizer-decl "[csequence -> boolean]"
               csequence_codt nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (is_finite inductive-decl "bool" csequence_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (nonempty_finite_csequence type-eq-decl nil csequence_props nil)
    (last const-decl "T" csequence_nth nil)
    (T formal-type-decl nil csequence_append nil)
    (is_finite_induction formula-decl nil csequence_props nil)
    (nth def-decl "T" csequence_nth nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (coreduce adt-def-decl "{c: csequence[T] |
         inj_empty?(op(x)) AND empty?(c) OR
          inj_nonempty?(op(x)) AND nonempty?(c)}"
     csequence_codt_coreduce nil)
    (append_struct const-decl "csequence_struct" csequence_append nil)
    (append_rest formula-decl nil csequence_append nil)
    (last_rest formula-decl nil csequence_nth nil)
    (append_finite application-judgement "nonempty_finite_csequence"
     csequence_append nil)
    (append_finite judgement-tcc nil csequence_append nil))
   shostak))
(append_extensionality 0
  (append_extensionality-1 nil 3513601717
   ("" (skosimp)
    (("" (case "is_finite(cseq1!1) AND is_finite(cseq2!1)")
      (("1" (flatten)
        (("1" (assert)
          (("1" (rewrite "append_finite_def")
            (("1" (rewrite "append_finite_def")
              (("1" (lemma "append_length")
                (("1" (inst-cp - "t!1" "cseq2!1")
                  (("1" (inst - "t!1" "cseq1!1")
                    (("1" (assert)
                      (("1" (use "insert_extensionality")
                        (("1" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (split)
        (("1" (rewrite "append_infinite_def")
          (("1" (rewrite "append_infinite_def")
            (("1" (use "append_finite" ("fseq" "cseq2!1"))
              (("1" (assert) nil nil)) nil))
            nil))
          nil)
         ("2" (rewrite "append_infinite_def")
          (("1" (rewrite "append_infinite_def") nil nil)
           ("2" (use "append_finite" ("fseq" "cseq1!1"))
            (("2" (use "append_infinite_def") (("2" (assert) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((is_finite inductive-decl "bool" csequence_props nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_append nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers 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)
    (has_length def-decl "bool" csequence_props nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (insert_extensionality formula-decl nil csequence_insert nil)
    (append_length formula-decl nil csequence_append nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (append_finite_def formula-decl nil csequence_append nil)
    (append_infinite_def formula-decl nil csequence_append nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (append_finite judgement-tcc nil csequence_append nil))
   shostak))
(append_some 0
  (append_some-1 nil 3513601925
   ("" (skolem!)
    (("" (case "is_finite(cseq!1)")
      (("1" (rewrite "append_finite_def")
        (("1" (rewrite "insert_some") (("1" (prop) nil nil)) nil)) nil)
       ("2" (rewrite "append_infinite_def") (("2" (prop) nil nil))
        nil))
      nil))
    nil)
   ((is_finite inductive-decl "bool" csequence_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_append nil)
    (insert_some formula-decl nil csequence_insert nil)
    (pred type-eq-decl nil defined_types nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (has_length def-decl "bool" csequence_props nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (append_finite_def formula-decl nil csequence_append nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (append_infinite_def formula-decl nil csequence_append nil))
   shostak))
(append_every 0
  (append_every-1 nil 3513602032
   ("" (skolem!)
    (("" (case "is_finite(cseq!1)")
      (("1" (rewrite "append_finite_def")
        (("1" (rewrite "insert_every") (("1" (prop) nil nil)) nil))
        nil)
       ("2" (rewrite "append_infinite_def") (("2" (prop) nil nil))
        nil))
      nil))
    nil)
   ((is_finite inductive-decl "bool" csequence_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (csequence type-decl nil csequence_codt nil)
    (T formal-type-decl nil csequence_append nil)
    (insert_every formula-decl nil csequence_insert nil)
    (pred type-eq-decl nil defined_types nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (has_length def-decl "bool" csequence_props nil)
    (length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
    (finite_csequence nonempty-type-eq-decl nil csequence_props nil)
    (append_finite_def formula-decl nil csequence_append nil)
    (infinite_csequence type-eq-decl nil csequence_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (append_infinite_def formula-decl nil csequence_append nil))
   shostak)))

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