|
(csequence_constant
(constant_cseq_TCC1 0
(constant_cseq_TCC1-1 nil 3513602349 ("" (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_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
nil))
(constant_cseq_TCC2 0
(constant_cseq_TCC2-1 nil 3513602349 ("" (termination-tcc) nil nil)
nil nil))
(constant_cseq_TCC3 0
(constant_cseq_TCC3-1 nil 3513602349
("" (expand "is_finite") (("" (propax) nil nil)) nil)
((is_finite inductive-decl "bool" csequence_props nil)) nil))
(constant_cseq_empty 0
(constant_cseq_empty-1 nil 3513602385
("" (skolem!)
(("" (expand "constant_cseq")
(("" (lift-if) (("" (ground) nil nil)) nil)) nil))
nil)
((constant_cseq def-decl "finite_csequence" csequence_constant nil)
(int_minus_int_is_int application-judgement "int" integers nil))
shostak))
(constant_cseq_1 0
(constant_cseq_1-1 nil 3513602407 ("" (grind) nil nil)
((constant_cseq def-decl "finite_csequence" csequence_constant nil)
(T formal-type-decl nil csequence_constant nil)
(singleton_cseq const-decl "(singleton_cseq?)" csequence_singleton
nil))
shostak))
(constant_cseq_first_TCC1 0
(constant_cseq_first_TCC1-1 nil 3513602349
("" (skosimp)
(("" (expand "constant_cseq") (("" (assert) nil nil)) nil)) nil)
((constant_cseq def-decl "finite_csequence" csequence_constant nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(constant_cseq_first 0
(constant_cseq_first-1 nil 3513602464
("" (skosimp)
(("" (expand "constant_cseq") (("" (assert) nil nil)) nil)) nil)
((constant_cseq def-decl "finite_csequence" csequence_constant nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
shostak))
(constant_cseq_rest_TCC1 0
(constant_cseq_rest_TCC1-1 nil 3513602349 ("" (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_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))
nil))
(constant_cseq_rest 0
(constant_cseq_rest-1 nil 3513602539
("" (skosimp)
(("" (expand "constant_cseq" 1 1) (("" (assert) nil nil)) nil))
nil)
((constant_cseq def-decl "finite_csequence" csequence_constant nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil))
shostak))
(constant_cseq_length 0
(constant_cseq_length-1 nil 3513602568
("" (induct "n")
(("1" (expand* "constant_cseq" "length") nil nil)
("2" (skosimp*)
(("2" (expand "constant_cseq" +)
(("2" (expand "length" +) (("2" (inst - "t!1") nil nil)) nil))
nil))
nil))
nil)
((nat_induction formula-decl nil naturalnumbers nil)
(constant_cseq def-decl "finite_csequence" csequence_constant 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)
(is_finite inductive-decl "bool" csequence_props nil)
(csequence type-decl nil csequence_codt nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(T formal-type-decl nil csequence_constant 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))
(constant_cseq_index 0
(constant_cseq_index-1 nil 3513602615
("" (skolem!)
(("" (rewrite "index?_finite")
(("" (rewrite "constant_cseq_length") (("" (prop) nil nil)) nil))
nil))
nil)
((index?_finite formula-decl nil 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)
(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)
(constant_cseq def-decl "finite_csequence" csequence_constant nil)
(T formal-type-decl nil csequence_constant nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(constant_cseq_length formula-decl nil csequence_constant nil))
shostak))
(constant_cseq_nth_TCC1 0
(constant_cseq_nth_TCC1-1 nil 3513602349
("" (skolem!)
(("" (rewrite "index?_finite")
(("" (rewrite "constant_cseq_length") (("" (assert) nil nil))
nil))
nil))
nil)
((index?_finite formula-decl nil 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)
(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)
(constant_cseq def-decl "finite_csequence" csequence_constant nil)
(< const-decl "bool" reals nil)
(below type-eq-decl nil nat_types nil)
(T formal-type-decl nil csequence_constant nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(constant_cseq_length formula-decl nil csequence_constant nil))
nil))
(constant_cseq_nth 0
(constant_cseq_nth-1 nil 3513602648
("" (induct "n")
(("1" (skolem-typepred) nil nil)
("2" (skosimp*)
(("2" (expand "constant_cseq" +)
(("2" (expand "nth" +)
(("2" (lift-if)
(("2" (ground) (("2" (inst - "t!1" "m!1 - 1") nil nil))
nil))
nil))
nil))
nil))
nil)
("3" (skolem!) (("3" (use "constant_cseq_nth_TCC1") nil nil))
nil))
nil)
((constant_cseq_nth_TCC1 subtype-tcc nil csequence_constant nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nat_induction formula-decl nil naturalnumbers nil)
(nth def-decl "T" csequence_nth nil)
(indexes type-eq-decl nil 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)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(T formal-type-decl nil csequence_constant nil)
(< const-decl "bool" reals nil)
(below type-eq-decl nil nat_types nil)
(csequence type-decl nil csequence_codt nil)
(index? def-decl "bool" csequence_nth nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(constant_cseq def-decl "finite_csequence" csequence_constant nil))
shostak))
(constant_cseq_add 0
(constant_cseq_add-1 nil 3513602705
("" (expand "constant_cseq" + 2) (("" (propax) nil nil)) nil)
((constant_cseq def-decl "finite_csequence" csequence_constant nil))
shostak))
(constant_cseq_last 0
(constant_cseq_last-1 nil 3513602720
("" (induct "n")
(("1" (skosimp) (("1" (assert) nil nil)) nil)
("2" (skosimp*)
(("2" (expand "constant_cseq" +)
(("2" (expand "last")
(("2" (expand "nth" +)
(("2" (expand "length" +)
(("2" (lift-if)
(("2" (inst - "t!1")
(("2" (expand "constant_cseq" 1 1)
(("2" (expand "length" 1 1)
(("2" (ground) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skosimp)
(("3" (use "constant_cseq_first_TCC1") (("3" (assert) nil nil))
nil))
nil))
nil)
((constant_cseq_first_TCC1 subtype-tcc nil csequence_constant nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(nth def-decl "T" csequence_nth nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nat_induction formula-decl nil naturalnumbers nil)
(last const-decl "T" csequence_nth nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props 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)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(T formal-type-decl nil csequence_constant nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(> const-decl "bool" reals nil)
(csequence type-decl nil csequence_codt nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(constant_cseq def-decl "finite_csequence" csequence_constant nil))
shostak))
(constant_cseq_some 0
(constant_cseq_some-1 nil 3513603136
("" (induct "n")
(("1" (expand* "constant_cseq" "some") nil nil)
("2" (skosimp*)
(("2" (inst - "t!1" "p!1")
(("2" (expand "constant_cseq" +)
(("2" (expand "some" +) (("2" (ground) nil nil)) nil)) nil))
nil))
nil))
nil)
((nat_induction formula-decl nil naturalnumbers nil)
(> const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(constant_cseq def-decl "finite_csequence" csequence_constant nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(some inductive-decl "boolean" csequence_codt nil)
(csequence type-decl nil csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(T formal-type-decl nil csequence_constant 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))
(constant_cseq_every 0
(constant_cseq_every-1 nil 3513603181
("" (induct "n")
(("1" (expand* "constant_cseq" "every") nil nil)
("2" (skosimp*)
(("2" (inst - "t!1" "p!1")
(("2" (expand "constant_cseq" +)
(("2" (expand "every" +) (("2" (ground) nil nil)) nil)) nil))
nil))
nil))
nil)
((nat_induction formula-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(constant_cseq def-decl "finite_csequence" csequence_constant nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(every coinductive-decl "boolean" csequence_codt nil)
(csequence type-decl nil csequence_codt nil)
(PRED type-eq-decl nil defined_types nil)
(IFF const-decl "[bool, bool -> bool]" booleans nil)
(T formal-type-decl nil csequence_constant 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))
(constant_cseq_TCC4 0
(constant_cseq_TCC4-1 nil 3513602349
("" (skolem!)
(("" (rewrite "is_finite_def")
(("" (rewrite "not_exists")
(("" (induct "x")
(("1"
(expand* "has_length" "constant_cseq_struct" "coreduce")
nil nil)
("2" (skosimp)
(("2" (expand "constant_cseq_struct")
(("2" (expand "coreduce" -)
(("2" (expand "has_length" -) (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((is_finite_def formula-decl nil csequence_props nil)
(csequence type-decl nil csequence_codt nil)
(csequence_struct type-decl nil csequence_codt_coreduce nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(inj_empty? adt-recognizer-decl "[csequence_struct -> boolean]"
csequence_codt_coreduce nil)
(empty? adt-recognizer-decl "[csequence -> boolean]" csequence_codt
nil)
(inj_nonempty? adt-recognizer-decl "[csequence_struct -> boolean]"
csequence_codt_coreduce nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
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)
(constant_cseq_struct const-decl "csequence_struct[T, T]"
csequence_constant nil)
(T formal-type-decl nil csequence_constant nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(pred type-eq-decl nil defined_types nil)
(nat_induction formula-decl nil naturalnumbers 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)
(has_length def-decl "bool" csequence_props nil)
(not_exists formula-decl nil quantifier_props nil))
nil))
(constant_cseq_inf_first 0
(constant_cseq_inf_first-1 nil 3513603454
("" (expand* "constant_cseq" "constant_cseq_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)
(constant_cseq_struct const-decl "csequence_struct[T, T]"
csequence_constant nil)
(constant_cseq const-decl "infinite_csequence" csequence_constant
nil))
shostak))
(constant_cseq_inf_rest 0
(constant_cseq_inf_rest-1 nil 3513603484
("" (expand* "constant_cseq" "constant_cseq_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)
(constant_cseq const-decl "infinite_csequence" csequence_constant
nil)
(constant_cseq_struct const-decl "csequence_struct[T, T]"
csequence_constant nil))
shostak))
(constant_cseq_inf_nth_TCC1 0
(constant_cseq_inf_nth_TCC1-1 nil 3513602349
("" (skolem!) (("" (use "index?_infinite") nil nil)) 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)
(constant_cseq const-decl "infinite_csequence" csequence_constant
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)
(index?_infinite formula-decl nil csequence_nth nil)
(T formal-type-decl nil csequence_constant nil))
nil))
(constant_cseq_inf_nth 0
(constant_cseq_inf_nth-1 nil 3513603542
("" (induct "n")
(("1"
(expand* "nth" "constant_cseq" "constant_cseq_struct" "coreduce")
nil nil)
("2" (skosimp*)
(("2" (inst - "t!1")
(("2" (expand "nth" +)
(("2" (expand* "constant_cseq" "constant_cseq_struct")
(("2" (expand "coreduce" +) (("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil)
("3" (skolem!) (("3" (use "constant_cseq_inf_nth_TCC1") nil nil))
nil))
nil)
((constant_cseq_inf_nth_TCC1 subtype-tcc nil csequence_constant nil)
(constant_cseq_struct const-decl "csequence_struct[T, T]"
csequence_constant 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)
(nat_induction formula-decl nil naturalnumbers nil)
(nth def-decl "T" csequence_nth nil)
(indexes type-eq-decl nil 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)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(T formal-type-decl nil csequence_constant nil)
(csequence type-decl nil csequence_codt nil)
(index? def-decl "bool" csequence_nth nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(constant_cseq const-decl "infinite_csequence" csequence_constant
nil))
shostak))
(constant_cseq_inf_add 0
(constant_cseq_inf_add-1 nil 3513603611
("" (expand* "constant_cseq" "constant_cseq_struct")
(("" (expand "coreduce" 1 2) (("" (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)
(constant_cseq const-decl "infinite_csequence" csequence_constant
nil)
(constant_cseq_struct const-decl "csequence_struct[T, T]"
csequence_constant nil))
shostak))
(constant_cseq_inf_some 0
(constant_cseq_inf_some-1 nil 3513603630
("" (skolem!)
(("" (prop)
(("1" (lemma "some_induction")
(("1"
(inst - "p!1"
"LAMBDA (cseq: csequence): FORALL t: cseq = constant_cseq(t) IMPLIES p!1(t)")
(("1" (split)
(("1" (inst - "constant_cseq(t!1)")
(("1" (assert) (("1" (inst - "t!1") nil nil)) nil)) nil)
("2" (delete -1 2)
(("2" (skosimp*)
(("2" (lift-if)
(("2" (ground)
(("1" (use "constant_cseq_inf_first")
(("1" (assert) nil nil)) nil)
("2" (inst - "t!2")
(("2" (replace -3)
(("2" (rewrite "constant_cseq_inf_rest") nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand* "constant_cseq" "constant_cseq_struct" "coreduce"
"some")
(("2" (flatten) nil nil)) nil))
nil))
nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(pred type-eq-decl nil defined_types nil)
(csequence type-decl nil csequence_codt nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(constant_cseq const-decl "infinite_csequence" csequence_constant
nil)
(constant_cseq_inf_rest formula-decl nil csequence_constant nil)
(constant_cseq_inf_first formula-decl nil csequence_constant nil)
(some_induction formula-decl nil csequence_codt nil)
(T formal-type-decl nil csequence_constant 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)
(some inductive-decl "boolean" csequence_codt nil)
(constant_cseq_struct const-decl "csequence_struct[T, T]"
csequence_constant nil))
shostak))
(constant_cseq_inf_every 0
(constant_cseq_inf_every-1 nil 3513603731
("" (skolem!)
(("" (rewrite "every_some_rew")
(("" (rewrite "constant_cseq_inf_some")
(("" (expand "pred_NOT") (("" (propax) nil nil)) nil)) nil))
nil))
nil)
((every_some_rew formula-decl nil csequence_props nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(pred type-eq-decl nil defined_types nil)
(csequence type-decl nil csequence_codt nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(is_finite inductive-decl "bool" csequence_props nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(constant_cseq const-decl "infinite_csequence" csequence_constant
nil)
(T formal-type-decl nil csequence_constant nil)
(constant_cseq_inf_some formula-decl nil csequence_constant nil)
(pred_NOT const-decl "bool" csequence_props nil))
shostak)))
¤ Dauer der Verarbeitung: 0.33 Sekunden
(vorverarbeitet)
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