|
(csequence_map_props
(map_empty 0
(map_empty-1 nil 3513550848 ("" (grind) nil nil)
((map adt-def-decl "csequence[T1]" csequence_codt_map nil))
shostak))
(map_nonempty 0
(map_nonempty-1 nil 3513550854 ("" (grind) nil nil)
((map adt-def-decl "csequence[T1]" csequence_codt_map nil))
shostak))
(map_finite 0
(map_finite-1 nil 3513550835
("" (skolem + ("f!1" "_"))
(("" (induct "fseq" :name "is_finite_induction[T1]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp)
(("3" (expand "map" +)
(("3" (expand "is_finite" +) (("3" (reduce) 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)
(is_finite inductive-decl "bool" csequence_props nil)
(T2 formal-type-decl nil csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(T1 formal-type-decl nil csequence_map_props nil)
(is_finite_induction formula-decl nil csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil))
nil))
(map_infinite 0
(map_infinite-1 nil 3513550835
("" (skolem + ("f!1" "_"))
((""
(measure-induct+
"IF is_finite[T2](map(f!1, iseq)) THEN length(map(f!1, iseq)) ELSE 0 ENDIF"
("iseq") :skolem-typepreds? t)
(("" (assert)
(("" (expand "is_finite" (-2 +))
(("" (expand "map" -2)
(("" (lift-if)
(("" (ground)
(("" (inst - "rest(x!1)")
(("" (assert)
(("" (expand "map" 4 2)
(("" (expand "length" 4 2)
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((pred type-eq-decl nil defined_types nil)
(well_founded? const-decl "bool" orders nil)
(measure_induction formula-decl nil measure_induction nil)
(T1 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans 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)
(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)
(naturalnumber type-eq-decl nil naturalnumbers nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(T2 formal-type-decl nil csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(has_length def-decl "bool" csequence_props nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(< const-decl "bool" reals nil)
(wf_nat formula-decl nil naturalnumbers nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil))
(map_first_TCC1 0
(map_first_TCC1-1 nil 3513550835
("" (skolem!) (("" (rewrite "map_nonempty") nil nil)) nil)
((map_nonempty formula-decl nil csequence_map_props nil)
(T1 formal-type-decl nil csequence_map_props nil)
(T2 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(nonempty_csequence type-eq-decl nil csequence_props nil))
nil))
(map_first 0
(map_first-1 nil 3513551066 ("" (grind) nil nil)
((map adt-def-decl "csequence[T1]" csequence_codt_map nil))
shostak))
(map_rest 0
(map_rest-1 nil 3513551075
("" (expand "map" 1 1) (("" (propax) nil nil)) nil)
((map adt-def-decl "csequence[T1]" csequence_codt_map nil))
shostak))
(map_length 0
(map_length-1 nil 3513551085
("" (skolem + ("f!1" "_"))
(("" (induct "fseq" :name "is_finite_induction[T1]")
(("1" (assert) nil nil) ("2" (assert) nil nil)
("3" (skosimp)
(("3" (ground)
(("1" (use "map_empty")
(("1" (expand "length") (("1" (assert) nil nil)) nil)) nil)
("2" (expand "map" +)
(("2" (expand "length" +) (("2" (reduce) nil nil)) nil))
nil))
nil))
nil)
("4" (skosimp) (("4" (rewrite "map_finite") nil nil)) nil))
nil))
nil)
((f!1 skolem-const-decl "[T1 -> T2]" csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(T2 formal-type-decl nil csequence_map_props 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)
(number nonempty-type-decl nil numbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(has_length def-decl "bool" csequence_props nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(T1 formal-type-decl nil csequence_map_props nil)
(is_finite_induction formula-decl nil csequence_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(map_empty formula-decl nil csequence_map_props nil)
(map_finite judgement-tcc nil csequence_map_props nil))
shostak))
(map_index 0
(map_index-1 nil 3513551180
("" (skolem!)
(("" (decompose-equality)
(("" (rewrite "index?_prop[T1]")
(("" (rewrite "index?_prop[T2]")
(("" (iff)
(("" (rewrite "map_length")
(("" (ground)
(("1" (rewrite "map_finite") nil nil)
("2" (rewrite "map_infinite") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T2 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil)
(index? def-decl "bool" csequence_nth nil)
(T1 formal-type-decl nil csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map 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)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(is_finite inductive-decl "bool" csequence_props nil)
(map_length formula-decl nil csequence_map_props nil)
(infinite_csequence type-eq-decl nil csequence_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(map_infinite judgement-tcc nil csequence_map_props nil)
(map_finite judgement-tcc nil csequence_map_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(index?_prop formula-decl nil csequence_nth nil))
shostak))
(map_nth_TCC1 0
(map_nth_TCC1-1 nil 3513550835
("" (skolem!)
(("" (rewrite "map_index") (("" (assert) nil nil)) nil)) nil)
((map_index formula-decl nil csequence_map_props nil)
(T1 formal-type-decl nil csequence_map_props nil)
(T2 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil))
nil))
(map_nth 0
(map_nth-1 nil 3513551248
("" (skolem + ("f!1" "_" "_"))
(("" (measure-induct+ "n" ("cseq" "n") :skolem-typepreds? t)
(("1" (expand "map" +)
(("1" (lift-if)
(("1" (use "index?_nonempty[T1]")
(("1" (assert)
(("1" (expand "nth" +)
(("1" (lift-if)
(("1" (ground)
(("1" (inst - "rest(x!1)" "x!2 - 1")
(("1" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (rewrite "map_index") nil nil)
("3" (rewrite "map_index") (("3" (assert) nil nil)) nil)
("4" (rewrite "map_index") (("4" (assert) nil nil)) nil)
("5" (rewrite "map_index") nil nil))
nil))
nil)
((pred type-eq-decl nil defined_types nil)
(well_founded? const-decl "bool" orders nil)
(measure_induction formula-decl nil measure_induction nil)
(T1 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(index? def-decl "bool" csequence_nth nil)
(indexes type-eq-decl nil csequence_nth nil)
(naturalnumber type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil)
(wf_nat formula-decl nil naturalnumbers nil)
(f!1 skolem-const-decl "[T1 -> T2]" csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(T2 formal-type-decl nil csequence_map_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(nth def-decl "T" csequence_nth nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields 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)
(int_minus_int_is_int application-judgement "int" integers nil)
(index?_nonempty formula-decl nil csequence_nth nil)
(map_index formula-decl nil csequence_map_props nil))
shostak))
(map_add 0
(map_add-1 nil 3513551339
("" (expand "map" 1 2) (("" (propax) nil nil)) nil)
((map adt-def-decl "csequence[T1]" csequence_codt_map nil))
shostak))
(map_last_TCC1 0
(map_last_TCC1-1 nil 3513550835
("" (skolem!) (("" (rewrite "map_nonempty") nil nil)) nil)
((map_nonempty formula-decl nil csequence_map_props nil)
(T1 formal-type-decl nil csequence_map_props nil)
(T2 formal-type-decl nil csequence_map_props 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)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props nil))
nil))
(map_last 0
(map_last-1 nil 3513551375
("" (auto-rewrite "map_length")
(("" (skolem-typepred)
(("" (expand "last")
(("" (rewrite "map_nth")
(("" (rewrite "length_nonempty?_rew[T1]")
(("" (assert) (("" (rewrite "index?_finite") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(T1 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil)
(is_finite inductive-decl "bool" csequence_props nil)
(finite_csequence nonempty-type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(nonempty_finite_csequence type-eq-decl nil csequence_props nil)
(map_length formula-decl nil csequence_map_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(map_finite application-judgement "finite_csequence[T2]"
csequence_map_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(map_nth formula-decl nil csequence_map_props nil)
(T2 formal-type-decl nil csequence_map_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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(has_length def-decl "bool" csequence_props nil)
(length def-decl "{n | has_length(fseq, n)}" csequence_length nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(index?_finite formula-decl nil csequence_nth 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)
(length_nonempty?_rew formula-decl nil csequence_length nil)
(last const-decl "T" csequence_nth nil))
shostak))
(map_map 0
(map_map-1 nil 3513551441
("" (skolem!)
(("" (lemma "coinduction[T2]")
((""
(inst -
"LAMBDA (cseq1, cseq2: csequence[T2]): EXISTS cseq: cseq1 = map(f!1)(cseq) AND cseq2 = map(f!1, cseq)"
"map(f!1)(cseq!1)" "map(f!1, cseq!1)")
(("1" (assert) (("1" (inst + "cseq!1") nil nil)) nil)
("2" (delete 2)
(("2" (expand "bisimulation?")
(("2" (skosimp*)
(("2" (expand "map" -)
(("2" (replace*)
(("2" (hide -1 -2)
(("2" (smash)
(("2" (inst + "rest(cseq!2)") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((T2 formal-type-decl nil csequence_map_props nil)
(coinduction formula-decl nil csequence_codt nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(csequence type-decl nil csequence_codt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(bisimulation? adt-def-decl "boolean" csequence_codt nil)
(T1 formal-type-decl nil csequence_map_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(f!1 skolem-const-decl "[T1 -> T2]" csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil))
shostak))
(map_injective 0
(map_injective-1 nil 3513551608
("" (expand "injective?")
(("" (skosimp*)
(("" (lemma "coinduction[T1]")
((""
(inst -
"LAMBDA cseq1, cseq2: map(f!1)(cseq1) = map(f!1)(cseq2)"
"x1!1" "x2!1")
(("1" (assert) nil nil)
("2" (delete -2 2)
(("2" (expand "bisimulation?")
(("2" (skosimp)
(("2" (expand "map" -)
(("2" (reduce)
(("1" (decompose-equality) nil nil)
("2" (decompose-equality) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((f!1 skolem-const-decl "[T1 -> T2]" csequence_map_props nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(T2 formal-type-decl nil csequence_map_props 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)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(add adt-constructor-decl "[[T, csequence] -> (nonempty?)]"
csequence_codt nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(first adt-accessor-decl "[(nonempty?) -> T]" csequence_codt nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(coinduction formula-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_map_props nil)
(injective? const-decl "bool" functions nil))
shostak))
(map_extensionality 0
(map_extensionality-1 nil 3513551776
("" (skosimp)
(("" (forward-chain "map_injective")
(("" (expand "injective?" -1)
(("" (inst - "cseq1!1" "cseq2!1")
(("" (assert)
(("" (rewrite "map_map") (("" (rewrite "map_map") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((map_injective formula-decl nil csequence_map_props nil)
(T1 formal-type-decl nil csequence_map_props nil)
(T2 formal-type-decl nil csequence_map_props nil)
(csequence type-decl nil csequence_codt nil)
(map_map formula-decl nil csequence_map_props nil)
(injective? const-decl "bool" functions nil))
shostak))
(map_some 0
(map_some-1 nil 3513551820
("" (skolem!)
(("" (prop)
(("1" (lemma "some_induction[T2]")
(("1"
(inst - "p!1"
"LAMBDA (cseq2: csequence[T2]): FORALL cseq: cseq2 = map(f!1, cseq) IMPLIES some(p!1 o f!1)(cseq)")
(("1" (split)
(("1" (inst - "map(f!1, cseq!1)")
(("1" (assert) (("1" (inst - "cseq!1") nil nil)) nil))
nil)
("2" (delete -1 2)
(("2" (skosimp*)
(("2" (replace -2)
(("2" (hide -2)
(("2" (lift-if)
(("2" (ground)
(("1" (expand* "map" "o" "some")
(("1" (reduce) nil nil)) nil)
("2" (use "map_empty")
(("2" (assert)
(("2" (rewrite "map_rest")
(("2"
(inst - "rest(cseq!2)")
(("2"
(expand "some" +)
(("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "some_induction[T1]")
(("2"
(inst - "p!1 o f!1" "LAMBDA cseq: some(p!1)(map(f!1, cseq))")
(("2" (split)
(("1" (inst - "cseq!1") (("1" (assert) nil nil)) nil)
("2" (delete -1 2)
(("2" (skosimp)
(("2" (lift-if)
(("2" (ground)
(("1" (expand* "map" "o" "some")
(("1" (flatten) nil nil)) nil)
("2" (use "map_empty" ("cseq" "a!1"))
(("2" (assert)
(("2" (expand "some" +)
(("2" (flatten)
(("2" (rewrite "map_rest") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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)
(T1 formal-type-decl nil csequence_map_props nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(some inductive-decl "boolean" csequence_codt nil)
(O const-decl "T3" function_props nil)
(map_empty formula-decl nil csequence_map_props nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(map_rest formula-decl nil csequence_map_props nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil)
(some_induction formula-decl nil csequence_codt nil)
(T2 formal-type-decl nil csequence_map_props nil))
shostak))
(map_every 0
(map_every-1 nil 3513551969
("" (skolem!)
(("" (prop)
(("1" (lemma "every_coinduction[T1]")
(("1"
(inst - "p!1 o f!1"
"LAMBDA cseq: every(p!1)(map(f!1, cseq))")
(("1" (split)
(("1" (inst - "cseq!1") (("1" (assert) nil nil)) nil)
("2" (delete -1 2)
(("2" (skosimp)
(("2" (lift-if)
(("2" (ground)
(("1" (expand* "map" "o" "every")
(("1" (flatten) nil nil)) nil)
("2" (use "map_empty" ("cseq" "a!1"))
(("2" (assert)
(("2" (expand "every" -)
(("2" (flatten)
(("2" (rewrite "map_rest") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "every_coinduction[T2]")
(("2"
(inst - "p!1"
"LAMBDA (cseq2: csequence[T2]): EXISTS cseq: cseq2 = map(f!1, cseq) AND every(p!1 o f!1)(cseq)")
(("2" (split)
(("1" (inst - "map(f!1, cseq!1)")
(("1" (assert) (("1" (inst + "cseq!1") nil nil)) nil))
nil)
("2" (delete -1 2)
(("2" (skosimp*)
(("2" (replace -1)
(("2" (hide -1)
(("2" (lift-if)
(("2" (ground)
(("1" (expand* "map" "o" "every")
(("1" (reduce) nil nil)) nil)
("2" (use "map_empty")
(("2" (assert)
(("2" (rewrite "map_rest")
(("2"
(inst + "rest(cseq!2)")
(("2"
(expand "every" -)
(("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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)
(T2 formal-type-decl nil csequence_map_props nil)
(O const-decl "T3" function_props nil)
(pred type-eq-decl nil defined_types nil)
(csequence type-decl nil csequence_codt nil)
(every coinductive-decl "boolean" csequence_codt nil)
(map adt-def-decl "csequence[T1]" csequence_codt_map nil)
(map_empty formula-decl nil csequence_map_props nil)
(nonempty_csequence type-eq-decl nil csequence_props nil)
(nonempty? adt-recognizer-decl "[csequence -> boolean]"
csequence_codt nil)
(map_rest formula-decl nil csequence_map_props nil)
(every_coinduction formula-decl nil csequence_codt nil)
(T1 formal-type-decl nil csequence_map_props nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(rest adt-accessor-decl "[(nonempty?) -> csequence]" csequence_codt
nil))
shostak)))
¤ Dauer der Verarbeitung: 0.31 Sekunden
(vorverarbeitet)
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