|
(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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