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nil))
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nil))
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nil))
nil))
nil))
nil))
nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
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("" (induct "index")
(("1" (skolem-typepred)
(("1" (expand "insert")
(("1" (expand "is_finite" -) (("1" (propax) nil nil)) nil))
nil))
nil)
("2" (skosimp* t)
(("2" (expand "insert" -3)
(("2" (expand "is_finite" (-3 +))
(("2" (ground) (("2" (inst - "rest(iseq!1)" "t!1") nil nil))
nil))
nil))
nil))
nil))
nil)
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(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))
nil))
(insert_first 0
(insert_first-1 nil 3513474782
("" (expand "insert") (("" (propax) nil nil)) nil)
((insert def-decl "nonempty_csequence" csequence_insert nil))
shostak))
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(insert_rest-1 nil 3513474789
("" (expand "insert" 1 1) (("" (propax) nil nil)) nil)
((insert def-decl "nonempty_csequence" csequence_insert nil))
shostak))
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("" (induct "index")
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(("2" (inst - "rest(fseq!1)" "t!1")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((length_empty?_rew formula-decl nil csequence_length nil)
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nil)
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(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(insert_finite application-judgement "nonempty_finite_csequence"
csequence_insert nil))
shostak))
(insert_index_TCC1 0
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((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
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
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nil))
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("" (auto-rewrite "index?_prop")
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("3" (use "insert_infinite") (("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
((index?_prop formula-decl nil csequence_nth nil)
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(real_lt_is_strict_total_order name-judgement
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real_props nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(insert_infinite judgement-tcc nil csequence_insert nil))
shostak))
(insert_nth_TCC1 0
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("" (skolem!)
(("" (rewrite "insert_index")
(("" (lift-if)
(("" (ground)
(("" (use "index?_lt" ("n" "n!1 - 1"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
((nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(insert_index formula-decl nil csequence_insert nil)
(T formal-type-decl nil csequence_insert nil)
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(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)
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(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)
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
(csequence type-decl nil csequence_codt nil)
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(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil)
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(< const-decl "bool" reals nil)
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(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(index?_lt formula-decl nil csequence_nth nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(insert_nth 0
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("" (induct "index")
(("1" (skolem!)
(("1" (expand "insert")
(("1" (expand "nth" 1 2) (("1" (propax) nil nil)) nil)) nil))
nil)
("2" (skosimp*)
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(("2" (expand "nth" +)
(("2" (use "index?_0")
(("2" (use "index?_lt")
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(("2" (lift-if)
(("2" (ground)
(("2" (inst - "rest(cseq!1)" "t!1" "n!1 - 1")
(("2" (lift-if)
(("2" (lift-if)
(("2" (lift-if) (("2" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skolem!) (("3" (use "insert_nth_TCC1") nil nil)) nil))
nil)
((insert_nth_TCC1 subtype-tcc nil csequence_insert nil)
(index?_lt formula-decl nil csequence_nth nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(index?_0 formula-decl nil csequence_nth nil)
(nat_induction formula-decl nil naturalnumbers nil)
(nth def-decl "T" csequence_nth nil)
(= const-decl "[T, T -> boolean]" equalities 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)
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(real nonempty-type-from-decl nil reals nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(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 csequence_insert nil)
(csequence type-decl nil csequence_codt nil)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
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(nonempty_csequence type-eq-decl nil csequence_props nil)
(insert def-decl "nonempty_csequence" csequence_insert nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(< const-decl "bool" reals nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
shostak))
(insert_0 0
(insert_0-1 nil 3513476241
("" (expand "insert") (("" (propax) nil nil)) nil)
((insert def-decl "nonempty_csequence" csequence_insert nil))
shostak))
(insert_add 0
(insert_add-1 nil 3513476246
("" (expand "insert" 1 2) (("" (propax) nil nil)) nil)
((insert def-decl "nonempty_csequence" csequence_insert nil))
shostak))
(insert_last_TCC1 0
(insert_last_TCC1-1 nil 3513474439
("" (skosimp) (("" (use "index?_nonempty") nil nil)) nil)
((csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props 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)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil)
(index!1 skolem-const-decl "nat" csequence_insert nil)
(fseq!1 skolem-const-decl "finite_csequence[T]" csequence_insert
nil)
(index?_nonempty formula-decl nil csequence_nth nil)
(T formal-type-decl nil csequence_insert nil))
nil))
(insert_last 0
(insert_last-1 nil 3513476319
("" (induct "fseq" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp*)
(("3" (ground)
(("1"
(expand* "insert" "index?" "last" "nth" "length" "length")
nil nil)
("2" (expand "insert" +)
(("2" (expand "last")
(("2" (expand "nth" +)
(("2" (expand "length" +)
(("2" (expand "length" 1 2)
(("2" (expand "index?" +)
(("2" (use "length_empty?_rew")
(("2" (smash)
(("1" (expand "nth" +) (("1" (propax) nil nil))
nil)
("2" (expand "nth" 4 1)
(("2" (propax) nil nil)) nil)
("3"
(lemma "length_empty?_rew"
("cseq"
"insert(t!1, index!1 - 1, rest(cseq!1))"))
(("3" (assert)
(("3"
(use "insert_finite"
("fseq"
"rest(cseq!1)"
"index"
"index!1 - 1"))
nil nil))
nil))
nil)
("4"
(lemma "length_empty?_rew"
("cseq"
"insert(t!1, index!1 - 1, rest(cseq!1))"))
(("4" (assert)
(("4"
(use "insert_finite"
("fseq"
"rest(cseq!1)"
"index"
"index!1 - 1"))
nil nil))
nil))
nil)
("5"
(lemma "length_empty?_rew"
("cseq" "rest(cseq!1)"))
(("5" (assert)
(("5" (expand "index?")
(("5" (propax) nil nil)) nil))
nil))
nil)
("6" (inst - "t!1" "index!1 - 1")
(("6" (assert) nil nil)) nil)
("7" (inst - "t!1" "index!1 - 1")
(("7" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4" (skosimp*) (("4" (use "index?_nonempty") nil nil)) nil)
("5" (skosimp*)
(("5" (use "insert_finite" ("fseq" "fseq!2")) nil nil)) nil))
nil)
((index?_nonempty formula-decl nil csequence_nth nil)
(index!1 skolem-const-decl "nat" csequence_insert nil)
(fseq!2 skolem-const-decl "csequence[T]" csequence_insert nil)
(indexes type-eq-decl nil csequence_nth nil)
(length_empty?_rew formula-decl nil csequence_length nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(insert_finite judgement-tcc nil csequence_insert nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nth def-decl "T" csequence_nth nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T formal-type-decl nil csequence_insert nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(last const-decl "T" csequence_nth nil)
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(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(index? def-decl "bool" csequence_nth 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)
(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)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(insert def-decl "nonempty_csequence" csequence_insert nil))
shostak))
(insert_beyond 0
(insert_beyond-1 nil 3513476824
("" (induct "fseq" :name "is_finite_induction")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp*)
(("3" (expand "insert" +)
(("3" (lift-if)
(("3" (lift-if)
(("3" (ground)
(("3" (rewrite "length_empty?_rew")
(("3" (decompose-equality 3)
(("3" (inst - "t!1" "index!1 - 1")
(("3" (expand "length" (-4 1))
(("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(cseq!1 skolem-const-decl "csequence[T]" csequence_insert nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(csequence_add_extensionality formula-decl nil csequence_codt nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers 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_insert nil)
(insert def-decl "nonempty_csequence" csequence_insert 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)
(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 "bool" reals 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)
(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))
(insert_insert_TCC1 0
(insert_insert_TCC1-1 nil 3513474439 ("" (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)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(insert_insert 0
(insert_insert-1 nil 3513476975
("" (skolem + ("t!1" "u!1" "_" "_" "_"))
(("" (induct "n")
(("1" (skolem!)
(("1" (expand "insert" 1 1)
(("1" (expand "insert" 1 3)
(("1" (expand "insert" 1 4)
(("1" (reduce)
(("1" (expand "insert" 1 2) (("1" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (lemma "length_empty?_rew" ("cseq" "cseq!1"))
(("2" (hide 1)
(("2" (prop)
(("1" (reveal 1)
(("1" (assert)
(("1" (expand "insert" 1 2)
(("1" (expand "insert" 1 1)
(("1" (expand "insert" 1 3)
(("1" (expand "insert" 1 4)
(("1" (expand "insert" +)
(("1" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (reveal 1)
(("2" (expand "insert" +)
(("2" (smash)
(("1" (expand "insert" +) (("1" (propax) nil nil))
nil)
("2" (decompose-equality 2)
(("2" (expand "insert" 1 1)
(("2" (propax) nil nil)) nil))
nil)
("3" (decompose-equality 2)
(("3" (inst - "m!1 - 1" "rest(cseq!1)")
(("3" (expand "is_finite" +)
(("3" (assert) nil nil)) nil))
nil))
nil)
("4" (decompose-equality 3)
(("4" (inst - "m!1 - 1" "rest(cseq!1)")
(("4" (expand "is_finite" +)
(("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("3" (reveal 1)
(("3" (expand "length" 1)
(("3" (expand "insert" +)
(("3" (smash)
(("1" (expand "insert" +)
(("1" (propax) nil nil)) nil)
("2" (decompose-equality 2)
(("2" (expand "insert" 1 1)
(("2" (propax) nil nil)) nil))
nil)
("3" (decompose-equality 2)
(("3" (inst - "m!1 - 1" "rest(cseq!1)")
(("3" (expand "is_finite" -1)
(("3" (assert) nil nil)) nil))
nil))
nil)
("4" (decompose-equality 3)
(("4" (inst - "m!1 - 1" "rest(cseq!1)")
(("4" (assert) nil nil)) nil))
nil)
("5" (decompose-equality 4)
(("5" (inst - "m!1 - 1" "rest(cseq!1)")
(("5" (assert) nil nil)) nil))
nil)
("6" (decompose-equality 3)
(("6" (inst - "m!1 - 1" "rest(cseq!1)")
(("6" (assert) nil nil)) nil))
nil)
("7" (decompose-equality 4)
(("7" (inst - "m!1 - 1" "rest(cseq!1)")
(("7" (assert) nil nil)) nil))
nil)
("8" (decompose-equality 3)
(("8" (inst - "m!1 - 1" "rest(cseq!1)")
(("8" (expand "is_finite" +)
(("8" (assert) nil nil)) nil))
nil))
nil)
("9" (decompose-equality 4)
(("9" (inst - "m!1 - 1" "rest(cseq!1)")
(("9" (expand "is_finite" +)
(("9" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skosimp) (("3" (assert) nil nil)) nil))
nil))
nil)
((int_minus_int_is_int application-judgement "int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers 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)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(> const-decl "bool" reals nil)
(is_finite inductive-decl "bool" csequence_props nil)
(<= const-decl "bool" reals nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_insert 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)
(pred type-eq-decl nil defined_types 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)
(insert def-decl "nonempty_csequence" csequence_insert nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nat_induction formula-decl nil naturalnumbers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(length_empty?_rew formula-decl nil csequence_length nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(csequence_add_extensionality formula-decl nil csequence_codt nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil))
shostak))
(insert_extensionality 0
(insert_extensionality-1 nil 3513477483
("" (induct "index")
(("1" (expand "insert")
(("1" (skosimp) (("1" (decompose-equality) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (expand "insert" -2)
(("2" (lift-if)
(("2" (lift-if)
(("2" (lift-if)
(("2" (ground)
(("1" (decompose-equality) nil nil)
("2" (decompose-equality) nil nil)
("3" (decompose-equality)
(("3" (inst? -)
(("3" (decompose-equality 3) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((csequence_add_extensionality formula-decl nil csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nat_induction formula-decl nil naturalnumbers nil)
(insert def-decl "nonempty_csequence" csequence_insert 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)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_insert 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))
(insert_some 0
(insert_some-1 nil 3513477534
("" (induct "index")
(("1" (expand "insert")
(("1" (expand "some" 1 1) (("1" (propax) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (expand "some" +)
(("2" (expand "insert" +)
(("2" (lift-if)
(("2" (lift-if)
(("2" (lift-if)
(("2" (ground)
(("1" (expand "some" -1) (("1" (propax) nil nil))
nil)
("2" (inst - "p!1" "t!1" "rest(cseq!1)")
(("2" (assert) nil nil)) nil)
("3" (inst - "p!1" "t!1" "rest(cseq!1)")
(("3" (assert) nil nil)) nil)
("4" (inst - "p!1" "t!1" "rest(cseq!1)")
(("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nat_induction formula-decl nil naturalnumbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(insert def-decl "nonempty_csequence" csequence_insert nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(some inductive-decl "boolean" csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_insert 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))
(insert_every 0
(insert_every-1 nil 3513477592
("" (induct "index")
(("1" (expand "insert")
(("1" (expand "every" 1 1) (("1" (propax) nil nil)) nil)) nil)
("2" (skosimp*)
(("2" (expand "every" +)
(("2" (expand "insert" +)
(("2" (lift-if)
(("2" (lift-if)
(("2" (lift-if)
(("2" (ground)
(("1" (expand "every" +) (("1" (propax) nil nil))
nil)
("2" (inst - "p!1" "t!1" "rest(cseq!1)")
(("2" (assert) nil nil)) nil)
("3" (inst - "p!1" "t!1" "rest(cseq!1)")
(("3" (assert) nil nil)) nil)
("4" (inst - "p!1" "t!1" "rest(cseq!1)")
(("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nat_induction formula-decl nil naturalnumbers nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(insert def-decl "nonempty_csequence" csequence_insert nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(every coinductive-decl "boolean" csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(csequence type-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_insert 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)))
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