|
(csequence_zip
(zip_struct_TCC1 0
(zip_struct_TCC1-1 nil 3513771483 ("" (subtype-tcc) nil nil) nil
nil))
(zip_struct_TCC2 0
(zip_struct_TCC2-1 nil 3513771483 ("" (subtype-tcc) nil nil) nil
nil))
(zip_finite1 0
(zip_finite1-1 nil 3513771483
("" (induct "fseq1" :name "is_finite_induction[T1]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp*)
(("3" (expand "is_finite" +)
(("3" (expand* "zip" "zip_struct")
(("3" (expand "coreduce" +)
(("3" (smash) (("3" (inst - "rest(cseq2!1)") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
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)
(T1 formal-type-decl nil csequence_zip nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(T2 formal-type-decl nil csequence_zip 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))
(zip_finite2 0
(zip_finite2-1 nil 3513771483
("" (induct "fseq2" :name "is_finite_induction[T2]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp*)
(("3" (expand "is_finite" +)
(("3" (expand* "zip" "zip_struct")
(("3" (expand "coreduce" +)
(("3" (smash) (("3" (inst - "rest(cseq1!1)") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
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)
(T2 formal-type-decl nil csequence_zip nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(T1 formal-type-decl nil csequence_zip 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))
(zip_infinite 0
(zip_infinite-1 nil 3513771483
("" (lemma "is_finite_induction[[T1, T2]]")
((""
(inst -
"LAMBDA (cseq: csequence[[T1, T2]]): FORALL cseq1, cseq2: cseq = zip(cseq1, cseq2) IMPLIES (is_finite(cseq1) OR is_finite(cseq2))")
(("" (split)
(("1" (skolem!)
(("1" (inst - "zip(iseq1!1, iseq2!1)")
(("1" (assert)
(("1" (inst - "iseq1!1" "iseq2!1")
(("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (delete 2)
(("2" (skosimp*)
(("2" (replace -2)
(("2" (hide -2)
(("2" (expand "is_finite" +)
(("2" (ground)
(("1" (expand* "zip" "zip_struct" "coreduce") nil
nil)
("2" (expand* "zip" "zip_struct")
(("2" (expand "coreduce" -1)
(("2" (expand "coreduce" -2 1)
(("2"
(inst - "rest(cseq1!1)" "rest(cseq2!1)")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip 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)
(infinite_csequence type-eq-decl nil csequence_props nil)
(is_finite_induction formula-decl nil csequence_props nil)
(T1 formal-type-decl nil csequence_zip nil)
(T2 formal-type-decl nil csequence_zip nil))
nil))
(zip_nonempty 0
(zip_nonempty-1 nil 3513771483
("" (expand* "zip" "zip_struct" "coreduce") nil 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)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil))
nil))
(zip_empty 0
(zip_empty-1 nil 3513772246
("" (expand* "zip" "zip_struct" "coreduce") (("" (reduce) nil nil))
nil)
((zip const-decl "csequence[[T1, T2]]" csequence_zip 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)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil))
shostak))
(zip_first 0
(zip_first-1 nil 3513772259
("" (expand* "zip" "zip_struct" "coreduce") nil 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)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil))
shostak))
(zip_rest 0
(zip_rest-1 nil 3513772266
("" (expand* "zip" "zip_struct")
(("" (expand "coreduce" 1 1) (("" (propax) nil nil)) nil)) 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)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil))
shostak))
(zip_add 0
(zip_add-1 nil 3513772432
("" (expand* "zip" "zip_struct")
(("" (expand "coreduce" 1 1) (("" (propax) nil nil)) nil)) 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)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil))
shostak))
(zip_length_TCC1 0
(zip_length_TCC1-1 nil 3513771483
("" (skosimp) (("" (use "zip_infinite") nil nil)) nil)
((cseq1!1 skolem-const-decl "csequence[T1]" csequence_zip nil)
(cseq2!1 skolem-const-decl "csequence[T2]" csequence_zip nil)
(T2 formal-type-decl nil csequence_zip nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(NOT const-decl "[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)
(T1 formal-type-decl nil csequence_zip nil)
(zip_infinite judgement-tcc nil csequence_zip nil))
nil))
(zip_length 0
(zip_length-1 nil 3513772751
(""
(measure-induct+
"IF is_finite(zip(cseq1, cseq2)) THEN length(zip(cseq1, cseq2)) ELSE 0 ENDIF"
("cseq1" "cseq2"))
(("1" (expand* "zip" "zip_struct")
(("1" (expand "coreduce" (-2 +))
(("1" (expand "is_finite" (-2 +))
(("1" (expand "length" +)
(("1" (expand "min")
(("1" (expand "coreduce" -1 3)
(("1" (expand "coreduce" -1 4)
(("1" (expand "is_finite" -1 2)
(("1" (expand "length" -1 2)
(("1" (smash)
(("1" (inst - "rest(x!1)" "rest(x!2)")
(("1" (assert) nil nil)) nil)
("2" (inst - "rest(x!1)" "rest(x!2)")
(("2" (assert) nil nil)) nil)
("3" (inst - "rest(x!1)" "rest(x!2)")
(("3" (assert) nil nil)) nil)
("4" (inst - "rest(x!1)" "rest(x!2)")
(("4" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (use "zip_infinite") nil nil)
("3" (use "zip_infinite") nil nil)
("4" (use "zip_infinite") nil nil)
("5" (use "zip_infinite") nil nil))
nil)
((cseq1!1 skolem-const-decl "csequence[T1]" csequence_zip nil)
(cseq2!1 skolem-const-decl "csequence[T2]" csequence_zip nil)
(y!1 skolem-const-decl "[csequence[T1], csequence[T2]]"
csequence_zip nil)
(x!1 skolem-const-decl "[csequence[T1], csequence[T2]]"
csequence_zip nil)
(y!1 skolem-const-decl "csequence[T1]" csequence_zip nil)
(y!2 skolem-const-decl "csequence[T2]" csequence_zip nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(zip_infinite judgement-tcc nil csequence_zip nil)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt 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)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props 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)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(<= const-decl "bool" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(wf_nat formula-decl nil naturalnumbers nil)
(< const-decl "bool" reals 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)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(is_finite inductive-decl "bool" csequence_props nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(naturalnumber 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)
(T2 formal-type-decl nil csequence_zip nil)
(csequence type-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_zip nil)
(measure_induction formula-decl nil measure_induction nil)
(well_founded? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types nil))
shostak))
(zip_index 0
(zip_index-1 nil 3513778320
("" (induct "n")
(("1" (expand* "index?" "zip" "zip_struct" "coreduce")
(("1" (reduce) nil nil)) nil)
("2" (skosimp*)
(("2" (expand "index?" +)
(("2" (expand* "zip" "zip_struct")
(("2" (expand "coreduce" +) (("2" (reduce) nil nil)) nil))
nil))
nil))
nil))
nil)
((nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
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)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(index? def-decl "bool" csequence_nth nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(T2 formal-type-decl nil csequence_zip nil)
(csequence type-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_zip 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))
(zip_nth_TCC1 0
(zip_nth_TCC1-1 nil 3513771483
("" (skolem-typepred)
(("" (rewrite "zip_index") (("" (flatten) nil nil)) nil)) nil)
((zip_index formula-decl nil csequence_zip nil)
(indexes type-eq-decl nil csequence_nth nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip 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)
(T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(zip_nth_TCC2 0
(zip_nth_TCC2-1 nil 3513771483
("" (skolem-typepred)
(("" (rewrite "zip_index") (("" (flatten) nil nil)) nil)) nil)
((zip_index formula-decl nil csequence_zip nil)
(indexes type-eq-decl nil csequence_nth nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip 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)
(T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(zip_nth 0
(zip_nth-1 nil 3513778393
("" (measure-induct+ "n" ("cseq1" "cseq2" "n") :skolem-typepreds? t)
(("1" (use "zip_index")
(("1" (ground)
(("1" (use "index?_nonempty[T2]")
(("1" (use "index?_nonempty[T1]")
(("1" (expand "nth" +)
(("1" (lift-if)
(("1" (ground)
(("1" (expand* "zip" "zip_struct" "coreduce") nil
nil)
("2" (inst - "rest(x!1)" "rest(x!2)" "x!3 - 1")
(("1" (assert)
(("1" (expand* "zip" "zip_struct")
(("1" (expand "coreduce" +)
(("1" (propax) nil nil)) nil))
nil))
nil)
("2" (expand "index?" -6)
(("2" (flatten)
(("2" (expand* "zip" "zip_struct")
(("2" (expand "coreduce" -7)
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (use "zip_nth_TCC2") nil nil)
("3" (use "zip_nth_TCC1") nil nil)
("4" (use "zip_nth_TCC2") nil nil)
("5" (use "zip_nth_TCC1") nil nil)
("6" (use "zip_nth_TCC2") nil nil)
("7" (use "zip_nth_TCC1") nil nil)
("8" (use "zip_nth_TCC2") nil nil)
("9" (use "zip_nth_TCC1") nil nil))
nil)
((zip_nth_TCC1 subtype-tcc nil csequence_zip nil)
(zip_nth_TCC2 subtype-tcc nil csequence_zip nil)
(zip_index formula-decl nil csequence_zip nil)
(index?_nonempty formula-decl nil csequence_nth 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)
(zip_struct const-decl
"csequence_struct[[T1, T2], [csequence[T1], csequence[T2]]]"
csequence_zip nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(x!3 skolem-const-decl "indexes[[T1, T2]](zip(x!1, x!2))"
csequence_zip nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(x!2 skolem-const-decl "csequence[T2]" csequence_zip nil)
(x!1 skolem-const-decl "csequence[T1]" csequence_zip nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(nth def-decl "T" csequence_nth nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(wf_nat formula-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil)
(naturalnumber type-eq-decl nil naturalnumbers nil)
(indexes type-eq-decl nil csequence_nth nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(index? def-decl "bool" csequence_nth 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)
(T2 formal-type-decl nil csequence_zip nil)
(csequence type-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_zip nil)
(measure_induction formula-decl nil measure_induction nil)
(well_founded? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types nil))
shostak))
(zip_last_TCC1 0
(zip_last_TCC1-1 nil 3513771483 ("" (subtype-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
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csequence_codt nil)
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nil))
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nil))
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("" (skosimp)
(("" (expand "length_lt")
(("" (use "length_nonempty?_rew[T1]")
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("2" (use "index?_infinite[T2]") nil nil))
nil))
nil))
nil))
nil)
((length_lt const-decl "bool" csequence_length_comp nil)
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real_props nil)
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"(strict_total_order?[real])" real_props nil)
(zip_nonempty application-judgement "nonempty_csequence[[T1, T2]]"
csequence_zip nil)
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(infinite_csequence type-eq-decl nil csequence_props nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
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(>= const-decl "bool" reals nil)
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(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(nseq2!1 skolem-const-decl "nonempty_csequence[T2]" csequence_zip
nil)
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(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
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(T1 formal-type-decl nil csequence_zip nil)
(length_nonempty?_rew formula-decl nil csequence_length nil))
nil))
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(zip_last_TCC4-1 nil 3513771483 ("" (subtype-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
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csequence_codt nil)
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(length_lt const-decl "bool" csequence_length_comp nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil))
nil))
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(zip_last_TCC5-1 nil 3513771483
("" (skosimp)
(("" (expand "length_gt")
(("" (use "length_nonempty?_rew[T2]")
(("" (ground)
(("1" (use "index?_infinite[T1]")
(("1" (rewrite "index?_finite[T1]") nil nil)) nil)
("2" (use "index?_infinite[T1]") nil nil))
nil))
nil))
nil))
nil)
((length_gt const-decl "bool" csequence_length_comp nil)
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real_props nil)
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(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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csequence_zip nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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(infinite_csequence type-eq-decl nil csequence_props nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
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(>= const-decl "bool" reals nil)
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(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(nseq1!1 skolem-const-decl "nonempty_csequence[T1]" csequence_zip
nil)
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(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
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csequence_codt nil)
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(length_nonempty?_rew formula-decl nil csequence_length nil))
nil))
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csequence_codt nil)
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nil))
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("" (skosimp)
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nil))
nil)
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csequence_zip nil)
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csequence_codt nil)
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(nseq2!1 skolem-const-decl "nonempty_csequence[T2]" csequence_zip
nil)
(zip_infinite judgement-tcc nil csequence_zip nil))
nil))
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("" (skosimp)
(("" (assert)
(("" (use "zip_infinite")
(("" (expand "length_lt") (("" (propax) nil nil)) nil)) nil))
nil))
nil)
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csequence_zip nil)
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csequence_codt nil)
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(T2 formal-type-decl nil csequence_zip nil)
(nseq1!1 skolem-const-decl "nonempty_csequence[T1]" csequence_zip
nil)
(zip_infinite judgement-tcc nil csequence_zip nil))
nil))
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((boolean nonempty-type-decl nil booleans nil)
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csequence_codt nil)
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"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(length_gt const-decl "bool" csequence_length_comp nil))
nil))
(zip_last 0
(zip_last-1 nil 3513778776
("" (skosimp)
(("" (expand* "length_lt" "length_gt" "last")
(("" (use "length_empty?_rew[[T1, T2]]")
(("" (auto-rewrite "zip_nth")
(("" (auto-rewrite "zip_length")
(("" (reduce)
(("1" (expand "min") (("1" (propax) nil nil)) nil)
("2" (expand "min") (("2" (propax) nil nil)) nil)
("3" (rewrite "zip_length")
(("3" (expand "min")
(("3" (lift-if) (("3" (ground) nil nil)) nil)) nil))
nil)
("4" (rewrite "zip_length")
(("4" (expand "min") (("4" (propax) nil nil)) nil))
nil)
("5" (expand "min") (("5" (propax) nil nil)) nil)
("6" (use "zip_infinite") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((length_gt const-decl "bool" csequence_length_comp nil)
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csequence_zip nil)
(int_minus_int_is_int application-judgement "int" integers nil)
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real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(zip_length formula-decl nil csequence_zip nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nat_min application-judgement "{k: nat | k <= i AND k <= j}"
real_defs nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
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(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
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(T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(length_empty?_rew formula-decl nil csequence_length nil))
shostak))
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(zip_extensionality-1 nil 3513778991
("" (skosimp)
(("" (split)
(("1" (lemma "coinduction[T1]")
(("1"
(inst -
"LAMBDA (cseq1, cseq3: csequence[T1]): EXISTS (cseq2, cseq4: csequence[T2]): length_eq(cseq1, cseq2) AND length_eq(cseq3, cseq4) AND zip(cseq1, cseq2) = zip(cseq3, cseq4)"
"cseq1!1" "cseq3!1")
(("1" (assert)
(("1" (inst + "cseq2!1" "cseq4!1") (("1" (assert) nil nil))
nil))
nil)
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(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2"
(case "nonempty?(x!1) AND nonempty?(y!1) AND nonempty?(cseq2!2) AND nonempty?(cseq4!2)")
(("1" (smash)
(("1" (inst + "rest(cseq2!2)" "rest(cseq4!2)")
(("1" (lemma "length_eq_rest")
(("1" (inst-cp - "y!1" "cseq4!2")
(("1" (inst - "x!1" "cseq2!2")
(("1" (lemma "zip_rest")
(("1"
(inst-cp - "y!1" "cseq4!2")
(("1"
(inst - "x!1" "cseq2!2")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "zip_first")
(("2" (inst-cp - "y!1" "cseq4!2")
(("2" (inst - "x!1" "cseq2!2")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (hide 3)
(("2" (lemma "zip_empty")
(("2" (inst-cp - "y!1" "cseq4!2")
(("2" (inst - "x!1" "cseq2!2")
(("2" (expand "length_eq")
(("2" (lemma "length_empty?_rew[T2]")
(("2"
(inst-cp - "cseq4!2")
(("2"
(inst - "cseq2!2")
(("2"
(lemma "length_empty?_rew[T1]")
(("2"
(inst-cp - "y!1")
(("2"
(inst - "x!1")
(("2" (smash) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "coinduction[T2]")
(("2"
(inst -
"LAMBDA (cseq2, cseq4: csequence[T2]): EXISTS (cseq1, cseq3: csequence[T1]): length_eq(cseq1, cseq2) AND length_eq(cseq3, cseq4) AND zip(cseq1, cseq2) = zip(cseq3, cseq4)"
"cseq2!1" "cseq4!1")
(("1" (assert)
(("1" (inst + "cseq1!1" "cseq3!1") (("1" (assert) nil nil))
nil))
nil)
("2" (delete -1 -2 -3 2)
(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2"
(case "nonempty?(cseq1!2) AND nonempty?(cseq3!2) AND nonempty?(x!1) AND nonempty?(y!1)")
(("1" (smash)
(("1" (inst + "rest(cseq1!2)" "rest(cseq3!2)")
(("1" (lemma "length_eq_rest")
(("1" (inst-cp - "cseq3!2" "y!1")
(("1" (inst - "cseq1!2" "x!1")
(("1" (lemma "zip_rest")
(("1"
(inst-cp - "cseq3!2" "y!1")
(("1"
(inst - "cseq1!2" "x!1")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "zip_first")
(("2" (inst-cp - "cseq3!2" "y!1")
(("2" (inst - "cseq1!2" "x!1")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (hide 3)
(("2" (lemma "zip_empty")
(("2" (inst-cp - "cseq3!2" "y!1")
(("2" (inst - "cseq1!2" "x!1")
(("2" (expand "length_eq")
(("2" (lemma "length_empty?_rew[T2]")
(("2"
(inst-cp - "y!1")
(("2"
(inst - "x!1")
(("2"
(lemma "length_empty?_rew[T1]")
(("2"
(inst-cp - "cseq3!2")
(("2"
(inst - "cseq1!2")
(("2" (smash) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(length_eq const-decl "bool" csequence_length_comp nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(T2 formal-type-decl nil csequence_zip nil)
(bisimulation? adt-def-decl "boolean" csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(csequence type-decl nil csequence_codt nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(zip_first formula-decl nil csequence_zip nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(zip_rest formula-decl nil csequence_zip nil)
(length_eq_rest formula-decl nil csequence_length_comp nil)
(zip_empty formula-decl nil csequence_zip nil)
(length_empty?_rew formula-decl nil csequence_length nil)
(coinduction formula-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_zip nil))
shostak))
(zip_some_TCC1 0
(zip_some_TCC1-1 nil 3513771483 ("" (subtype-tcc) nil nil)
((T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(length_lt const-decl "bool" csequence_length_comp nil))
nil))
(zip_some_TCC2 0
(zip_some_TCC2-1 nil 3513771483 ("" (subtype-tcc) nil nil)
((T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(length_gt const-decl "bool" csequence_length_comp nil)
(length_lt const-decl "bool" csequence_length_comp nil))
nil))
(zip_some_TCC3 0
(zip_some_TCC3-1 nil 3513771483 ("" (cond-disjoint-tcc) nil nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(length_gt const-decl "bool" csequence_length_comp nil))
nil))
(zip_some 0
(zip_some-1 nil 3513779390
("" (skolem!)
(("" (use "nth_some[[T1, T2]]")
(("" (smash)
(("1" (skolem-typepred)
(("1" (rewrite "zip_index")
(("1" (prop)
(("1" (use "nth_some[T1]")
(("1" (assert)
(("1" (inst + "i!1")
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (inst + "i!1")
(("2" (rewrite "zip_nth")
(("2" (assert)
(("2" (rewrite "index?_finite") nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (skolem-typepred)
(("2" (rewrite "zip_index")
(("2" (prop)
(("1" (inst + "i!1")
(("1" (rewrite "zip_nth")
(("1" (assert)
(("1" (rewrite "index?_finite" -3) nil nil)) nil))
nil))
nil)
("2" (use "nth_some[T2]")
(("2" (assert)
(("2" (inst + "i!1")
(("2" (rewrite "zip_nth") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skolem-typepred)
(("3" (rewrite "zip_index")
(("3" (prop)
(("1" (use "nth_some[T1]")
(("1" (assert)
(("1" (inst + "i!1")
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (use "nth_some[T2]")
(("2" (assert)
(("2" (inst + "i!1")
(("2" (rewrite "zip_nth") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4" (use "nth_some[T1]")
(("4" (assert)
(("4" (skolem-typepred)
(("4" (inst + "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil)
("2" (rewrite "zip_index")
(("2" (expand "length_lt")
(("2" (prop)
(("1" (rewrite "index?_finite")
(("1" (rewrite "index?_finite")
(("1" (assert) nil nil)) nil))
nil)
("2" (use "index?_infinite[T2]") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("5" (skosimp :preds? t)
(("5" (inst + "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil)) nil))
nil)
("2" (rewrite "zip_index")
(("2" (rewrite "index?_finite[T1]") nil nil)) nil))
nil))
nil)
("6" (use "nth_some[T2]")
(("6" (assert)
(("6" (skolem-typepred)
(("6" (inst + "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil)
("2" (rewrite "zip_index")
(("2" (expand "length_lt")
(("2" (prop)
(("1" (use "index?_infinite[T1]") nil nil)
("2" (rewrite "index?_finite")
(("2" (rewrite "index?_finite")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("7" (use "nth_some[T1]")
(("7" (assert)
(("7" (skolem-typepred)
(("7" (inst + "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil)
("2" (rewrite "zip_index")
(("2" (expand "length_gt")
(("2" (prop)
(("1" (use "index?_infinite[T2]") nil nil)
("2" (rewrite "index?_finite")
(("2" (rewrite "index?_finite")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("8" (skosimp :preds? t)
(("8" (inst + "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil)) nil))
nil)
("2" (rewrite "zip_index")
(("2" (use "index?_finite[T2]") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nth_some formula-decl nil csequence_nth nil)
(T1 formal-type-decl nil csequence_zip nil)
(T2 formal-type-decl nil csequence_zip nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(pred type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(csequence type-decl nil csequence_codt nil)
(i!1 skolem-const-decl "indexes[T1](cseq1!1)" csequence_zip nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(length_gt const-decl "bool" csequence_length_comp nil)
(i!1 skolem-const-decl "indexes[T1](cseq1!1)" csequence_zip nil)
(i!1 skolem-const-decl "indexes[T2](cseq2!1)" csequence_zip nil)
(i!1 skolem-const-decl "indexes[T2](cseq2!1)" csequence_zip nil)
(index?_infinite formula-decl nil csequence_nth nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(i!1 skolem-const-decl "indexes[T1](cseq1!1)" csequence_zip nil)
(i!1 skolem-const-decl "indexes[[T1, T2]](zip(cseq1!1, cseq2!1))"
csequence_zip 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)
(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)
(zip_nth formula-decl nil csequence_zip nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(index?_finite formula-decl nil csequence_nth nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(i!1 skolem-const-decl "indexes[[T1, T2]](zip(cseq1!1, cseq2!1))"
csequence_zip nil)
(cseq1!1 skolem-const-decl "csequence[T1]" csequence_zip nil)
(cseq2!1 skolem-const-decl "csequence[T2]" csequence_zip nil)
(zip_index formula-decl nil csequence_zip nil))
shostak))
(zip_every_TCC1 0
(zip_every_TCC1-1 nil 3513771483 ("" (subtype-tcc) nil nil)
((T2 formal-type-decl nil csequence_zip nil)
(T1 formal-type-decl nil csequence_zip nil)
(length_lt const-decl "bool" csequence_length_comp nil))
nil))
(zip_every 0
(zip_every-1 nil 3513779764
("" (skolem!)
(("" (use "nth_every[[T1, T2]]")
(("" (smash)
(("1" (skosimp :preds? t)
(("1" (inst - "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil)) nil))
nil)
("2" (use "index?_finite[T1]")
(("2" (assert) (("2" (rewrite "zip_index") nil nil))
nil))
nil))
nil))
nil)
("2" (use "nth_every[T1]")
(("2" (assert)
(("2" (skolem-typepred)
(("2" (inst - "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil)
("2" (rewrite "zip_index")
(("2" (expand "length_lt")
(("2" (prop)
(("1" (rewrite "index?_finite")
(("1" (rewrite "index?_finite")
(("1" (assert) nil nil)) nil))
nil)
("2" (use "index?_infinite[T2]") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (use "nth_every[T2]")
(("3" (assert)
(("3" (skolem-typepred)
(("3" (inst - "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil)
("2" (rewrite "zip_index")
(("2" (expand "length_lt")
(("2" (prop)
(("1" (use "index?_infinite[T1]") nil nil)
("2" (rewrite "index?_finite")
(("2" (rewrite "index?_finite")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4" (skosimp :preds? t)
(("4" (inst - "i!1")
(("1" (rewrite "zip_nth") (("1" (assert) nil nil)) nil)
("2" (use "index?_finite[T2]")
(("2" (assert) (("2" (rewrite "zip_index") nil nil))
nil))
nil))
nil))
nil)
("5" (use "nth_every[T1]")
(("5" (assert)
(("5" (skolem-typepred)
(("5" (inst - "i!1")
(("1" (flatten)
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil)
("2" (rewrite "zip_index")
(("2" (expand "length_gt")
(("2" (prop)
(("1" (use "index?_infinite[T2]") nil nil)
("2" (rewrite "index?_finite")
(("2" (rewrite "index?_finite")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("6" (skolem-typepred)
(("6" (rewrite "zip_index")
(("6" (prop)
(("1" (use "nth_every[T1]")
(("1" (assert)
(("1" (inst - "i!1")
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (inst - "i!1")
(("2" (rewrite "zip_nth")
(("2" (assert)
(("2" (rewrite "index?_finite") nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("7" (skolem-typepred)
(("7" (rewrite "zip_index")
(("7" (prop)
(("1" (use "nth_every[T1]")
(("1" (assert)
(("1" (inst - "i!1")
(("1" (rewrite "zip_nth") (("1" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (use "nth_every[T2]")
(("2" (assert)
(("2" (inst - "i!1")
(("2" (rewrite "zip_nth") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("8" (skolem-typepred)
(("8" (rewrite "zip_index")
(("8" (prop)
(("1" (inst - "i!1")
(("1" (rewrite "zip_nth")
(("1" (assert)
(("1" (rewrite "index?_finite" -2) nil nil)) nil))
nil))
nil)
("2" (use "nth_every[T2]")
(("2" (assert)
(("2" (inst - "i!1")
(("2" (rewrite "zip_nth") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nth_every formula-decl nil csequence_nth nil)
(T1 formal-type-decl nil csequence_zip nil)
(T2 formal-type-decl nil csequence_zip nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(pred type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(zip const-decl "csequence[[T1, T2]]" csequence_zip nil)
(csequence type-decl nil csequence_codt nil)
(i!1 skolem-const-decl "indexes[[T1, T2]](zip(cseq1!1, cseq2!1))"
csequence_zip nil)
(i!1 skolem-const-decl "indexes[[T1, T2]](zip(cseq1!1, cseq2!1))"
csequence_zip nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(length_gt const-decl "bool" csequence_length_comp nil)
(i!1 skolem-const-decl "indexes[T1](cseq1!1)" csequence_zip nil)
(i!1 skolem-const-decl "indexes[T1](cseq1!1)" csequence_zip nil)
(i!1 skolem-const-decl "indexes[T2](cseq2!1)" csequence_zip nil)
(index?_infinite formula-decl nil csequence_nth nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(length_lt const-decl "bool" csequence_length_comp nil)
(i!1 skolem-const-decl "indexes[T1](cseq1!1)" csequence_zip 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(index?_finite formula-decl nil csequence_nth nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(zip_index formula-decl nil csequence_zip nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(zip_nth formula-decl nil csequence_zip nil)
(i!1 skolem-const-decl "indexes[T2](cseq2!1)" csequence_zip nil)
(cseq2!1 skolem-const-decl "csequence[T2]" csequence_zip nil)
(cseq1!1 skolem-const-decl "csequence[T1]" csequence_zip nil))
shostak)))
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