(total_lattices
(singleton_has_greatest 0
(singleton_has_greatest-1 nil 3316873516
("" (skolem!) (("" (use "non_empty_finite_has_greatest") nil nil))
nil)
((<= formal-const-decl "(total_order?[T])" total_lattices nil)
(total_order? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types nil)
(singleton const-decl "(singleton?)" sets nil)
(singleton? const-decl "bool" sets nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(empty? const-decl "bool" sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(finite_set type-eq-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(non_empty_finite_has_greatest formula-decl nil minmax_orders nil)
(T formal-type-decl nil total_lattices nil))
nil))
(union_preserves_has_greatest 0
(union_preserves_has_greatest-1 nil 3316872843
("" (skolem-typepred)
((""
(expand* "has_greatest?" "greatest?" "upper_bound?" "union"
"member")
(("" (skosimp*)
(("" (case "t!1 <= t!2")
(("1" (inst + "t!2")
(("1" (assert)
(("1" (skolem-typepred)
(("1" (expand* "union" "member")
(("1" (split)
(("1" (inst - "r!1")
(("1" (typepred "<=")
(("1"
(expand* "total_order?" "partial_order?"
"preorder?" "transitive?")
(("1" (flatten)
(("1" (inst - "r!1" "t!1" "t!2")
(("1" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (inst -6 "r!1") nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "<=")
(("2"
(expand* "total_order?" "dichotomous?" "partial_order?"
"preorder?" "transitive?")
(("2" (flatten)
(("2" (inst - "t!1" "t!2")
(("2" (inst + "t!1")
(("2" (assert)
(("2" (skolem-typepred)
(("2" (expand* "union" "member")
(("2" (split)
(("1" (inst - "r!1") nil nil)
("2" (inst -9 "r!1")
(("2"
(inst - "r!1" "t!2" "t!1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((greatest? const-decl "bool" minmax_orders nil)
(union const-decl "set" sets nil)
(member const-decl "bool" sets nil)
(upper_bound? const-decl "bool" bounded_orders nil)
(G1!1 skolem-const-decl
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(G2!1 skolem-const-decl
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(r!1 skolem-const-decl "(union[T](G1!1, G2!1))" total_lattices nil)
(partial_order? const-decl "bool" orders nil)
(transitive? const-decl "bool" relations nil)
(preorder? const-decl "bool" orders nil)
(dichotomous? const-decl "bool" orders nil)
(r!1 skolem-const-decl "(union[T](G1!1, G2!1))" total_lattices nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(total_order? const-decl "bool" orders nil)
(has_greatest? const-decl "bool" minmax_orders nil)
(pred type-eq-decl nil defined_types nil)
(set type-eq-decl nil sets nil)
(T formal-type-decl nil total_lattices nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(add_preserves_has_greatest 0
(add_preserves_has_greatest-1 nil 3316872843
("" (skolem!)
(("" (rewrite "add_as_union[T]") (("" (assert) nil nil)) nil)) nil)
((add_as_union formula-decl nil sets_lemmas nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(pred type-eq-decl nil defined_types nil)
(has_greatest? const-decl "bool" minmax_orders nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(T formal-type-decl nil total_lattices nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(nonempty_union2 application-judgement "(nonempty?)" total_lattices
nil)
(union_preserves_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil))
nil))
(greatest_singleton 0
(greatest_singleton-1 nil 3316873630
("" (skolem!)
(("" (rewrite "greatest_def")
(("" (grind)
(("" (typepred "<=")
((""
(expand* "total_order?" "partial_order?" "preorder?"
"reflexive?")
(("" (flatten) (("" (inst?) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(greatest_def formula-decl nil minmax_orders nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(antisymmetric? const-decl "bool" relations nil)
(pred type-eq-decl nil defined_types nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(set type-eq-decl nil sets nil)
(has_greatest? const-decl "bool" minmax_orders nil)
(singleton? const-decl "bool" sets nil)
(singleton const-decl "(singleton?)" sets nil)
(T formal-type-decl nil total_lattices nil)
(preorder? const-decl "bool" orders nil)
(reflexive? const-decl "bool" relations nil)
(partial_order? const-decl "bool" orders nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(upper_bound? const-decl "bool" bounded_orders nil)
(greatest? const-decl "bool" minmax_orders nil))
shostak))
(greatest_union 0
(greatest_union-1 nil 3316873738
("" (skolem!)
(("" (lift-if)
(("" (ground)
(("1" (rewrite "greatest_def")
(("1" (typepred "greatest(<=)(G2!1)")
(("1" (typepred "greatest(<=)(G1!1)")
(("1" (typepred "<=")
(("1" (grind :if-match nil)
(("1" (inst -7 "r!1")
(("1"
(inst - "r!1" "greatest(<=)(G1!1)"
"greatest(<=)(G2!1)")
(("1" (assert) nil nil)) nil))
nil)
("2" (inst -9 "r!1") nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "<=")
(("2" (expand* "total_order?" "dichotomous?")
(("2" (flatten)
(("2" (inst - "greatest(<=)(G1!1)" "greatest(<=)(G2!1)")
(("2" (assert)
(("2" (typepred "greatest(<=)(G2!1)")
(("2" (typepred "greatest(<=)(G1!1)")
(("2" (rewrite "greatest_def")
(("2" (grind :if-match nil)
(("1" (inst - "r!1") nil nil)
("2" (inst -5 "r!1")
(("2"
(inst - "r!1" "greatest(<=)(G2!1)"
"greatest(<=)(G1!1)")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((greatest_def formula-decl nil minmax_orders nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(antisymmetric? const-decl "bool" relations nil)
(pred type-eq-decl nil defined_types nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(set type-eq-decl nil sets nil)
(has_greatest? const-decl "bool" minmax_orders nil)
(greatest? const-decl "bool" minmax_orders nil)
(greatest const-decl "{t: (S) | greatest?(t, S, <=)}" minmax_orders
nil)
(union const-decl "set" sets nil)
(T formal-type-decl nil total_lattices nil)
(member const-decl "bool" sets nil)
(upper_bound? const-decl "bool" bounded_orders nil)
(dichotomous? const-decl "bool" orders nil)
(partial_order? const-decl "bool" orders nil)
(preorder? const-decl "bool" orders nil)
(transitive? const-decl "bool" relations nil)
(reflexive? const-decl "bool" relations nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(union_preserves_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil))
shostak))
(greatest_add 0
(greatest_add-1 nil 3316873976
("" (skolem!)
(("" (rewrite "add_as_union[T]")
(("" (use "greatest_union")
(("" (rewrite "greatest_singleton") nil nil)) nil))
nil))
nil)
((add_as_union formula-decl nil sets_lemmas nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(pred type-eq-decl nil defined_types nil)
(has_greatest? const-decl "bool" minmax_orders nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(T formal-type-decl nil total_lattices nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(nonempty_union2 application-judgement "(nonempty?)" total_lattices
nil)
(union_preserves_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(greatest_singleton formula-decl nil total_lattices nil)
(singleton const-decl "(singleton?)" sets nil)
(singleton? const-decl "bool" sets nil)
(greatest_union formula-decl nil total_lattices nil))
shostak))
(singleton_has_least 0
(singleton_has_least-1 nil 3316873516
("" (skolem!) (("" (use "non_empty_finite_has_least") nil nil)) nil)
((<= formal-const-decl "(total_order?[T])" total_lattices nil)
(total_order? const-decl "bool" orders nil)
(pred type-eq-decl nil defined_types nil)
(singleton const-decl "(singleton?)" sets nil)
(singleton? const-decl "bool" sets nil)
(non_empty_finite_set type-eq-decl nil finite_sets nil)
(empty? const-decl "bool" sets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(finite_set type-eq-decl nil finite_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(non_empty_finite_has_least formula-decl nil minmax_orders nil)
(T formal-type-decl nil total_lattices nil))
nil))
(union_preserves_has_least 0
(union_preserves_has_least-1 nil 3316872843
("" (skolem-typepred)
((""
(expand* "has_least?" "least?" "lower_bound?" "union" "member")
(("" (skosimp*)
(("" (case "t!1 <= t!2")
(("1" (inst + "t!1")
(("1" (assert)
(("1" (skolem-typepred)
(("1" (expand* "union" "member")
(("1" (split)
(("1" (inst - "r!1") nil nil)
("2" (inst -6 "r!1")
(("2" (typepred "<=")
(("2"
(expand* "total_order?" "partial_order?"
"preorder?" "transitive?")
(("2" (flatten)
(("2" (inst - "t!1" "t!2" "r!1")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "<=")
(("2"
(expand* "total_order?" "dichotomous?" "partial_order?"
"preorder?" "transitive?")
(("2" (flatten)
(("2" (inst - "t!1" "t!2")
(("2" (inst + "t!2")
(("2" (assert)
(("2" (skolem-typepred)
(("2" (expand* "union" "member")
(("2" (split)
(("1" (inst - "r!1")
(("1"
(inst - "t!2" "t!1" "r!1")
(("1" (assert) nil nil))
nil))
nil)
("2" (inst -9 "r!1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((least? const-decl "bool" minmax_orders nil)
(union const-decl "set" sets nil)
(member const-decl "bool" sets nil)
(lower_bound? const-decl "bool" bounded_orders nil)
(partial_order? const-decl "bool" orders nil)
(transitive? const-decl "bool" relations nil)
(preorder? const-decl "bool" orders nil)
(L1!1 skolem-const-decl "(LAMBDA (S: set[T]): has_least?(S, <=))"
total_lattices nil)
(L2!1 skolem-const-decl "(LAMBDA (S: set[T]): has_least?(S, <=))"
total_lattices nil)
(r!1 skolem-const-decl "(union[T](L1!1, L2!1))" total_lattices nil)
(dichotomous? const-decl "bool" orders nil)
(r!1 skolem-const-decl "(union[T](L1!1, L2!1))" total_lattices nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(total_order? const-decl "bool" orders nil)
(has_least? const-decl "bool" minmax_orders nil)
(pred type-eq-decl nil defined_types nil)
(set type-eq-decl nil sets nil)
(T formal-type-decl nil total_lattices nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(add_preserves_has_least 0
(add_preserves_has_least-1 nil 3316872843
("" (skolem!)
(("" (rewrite "add_as_union[T]") (("" (assert) nil nil)) nil)) nil)
((add_as_union formula-decl nil sets_lemmas nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(pred type-eq-decl nil defined_types nil)
(has_least? const-decl "bool" minmax_orders nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(T formal-type-decl nil total_lattices nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(singleton_has_least application-judgement
"(LAMBDA (S: set[T]): has_least?(S, <=))" total_lattices nil)
(nonempty_union2 application-judgement "(nonempty?)" total_lattices
nil)
(union_preserves_has_least application-judgement
"(LAMBDA (S: set[T]): has_least?(S, <=))" total_lattices nil))
nil))
(least_singleton 0
(least_singleton-1 nil 3316874553
("" (skolem!)
(("" (rewrite "least_def")
(("" (grind)
(("" (typepred "<=")
((""
(expand* "total_order?" "partial_order?" "preorder?"
"reflexive?")
(("" (flatten) (("" (inst?) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((singleton_has_least application-judgement
"(LAMBDA (S: set[T]): has_least?(S, <=))" total_lattices nil)
(singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(least_def formula-decl nil minmax_orders nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(antisymmetric? const-decl "bool" relations nil)
(pred type-eq-decl nil defined_types nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(set type-eq-decl nil sets nil)
(has_least? const-decl "bool" minmax_orders nil)
(singleton? const-decl "bool" sets nil)
(singleton const-decl "(singleton?)" sets nil)
(T formal-type-decl nil total_lattices nil)
(preorder? const-decl "bool" orders nil)
(reflexive? const-decl "bool" relations nil)
(partial_order? const-decl "bool" orders nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(lower_bound? const-decl "bool" bounded_orders nil)
(least? const-decl "bool" minmax_orders nil))
shostak))
(least_union 0
(least_union-1 nil 3316874582
("" (skolem!)
(("" (lift-if)
(("" (ground)
(("1" (rewrite "least_def")
(("1" (typepred "least(<=)(L2!1)")
(("1" (typepred "least(<=)(L1!1)")
(("1" (typepred "<=")
(("1" (grind :if-match nil)
(("1" (inst -7 "r!1") nil nil)
("2" (inst -9 "r!1")
(("2"
(inst - "least(<=)(L1!1)" "least(<=)(L2!1)"
"r!1")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "<=")
(("2" (expand* "total_order?" "dichotomous?")
(("2" (flatten)
(("2" (inst - "least(<=)(L1!1)" "least(<=)(L2!1)")
(("2" (assert)
(("2" (typepred "least(<=)(L2!1)")
(("2" (typepred "least(<=)(L1!1)")
(("2" (rewrite "least_def")
(("2" (grind :if-match nil)
(("1" (inst - "r!1")
(("1"
(inst - "least(<=)(L2!1)"
"least(<=)(L1!1)" "r!1")
(("1" (assert) nil nil)) nil))
nil)
("2" (inst -5 "r!1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((least_def formula-decl nil minmax_orders nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(PRED type-eq-decl nil defined_types nil)
(antisymmetric? const-decl "bool" relations nil)
(pred type-eq-decl nil defined_types nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(set type-eq-decl nil sets nil)
(has_least? const-decl "bool" minmax_orders nil)
(least? const-decl "bool" minmax_orders nil)
(least const-decl "{t: (S) | least?(t, S, <=)}" minmax_orders nil)
(union const-decl "set" sets nil)
(T formal-type-decl nil total_lattices nil)
(member const-decl "bool" sets nil)
(lower_bound? const-decl "bool" bounded_orders nil)
(dichotomous? const-decl "bool" orders nil)
(partial_order? const-decl "bool" orders nil)
(preorder? const-decl "bool" orders nil)
(transitive? const-decl "bool" relations nil)
(reflexive? const-decl "bool" relations nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(union_preserves_has_least application-judgement
"(LAMBDA (S: set[T]): has_least?(S, <=))" total_lattices nil))
shostak))
(least_add 0
(least_add-1 nil 3316874740
("" (skolem!)
(("" (rewrite "add_as_union[T]")
(("" (use "least_union")
(("" (rewrite "least_singleton") nil nil)) nil))
nil))
nil)
((add_as_union formula-decl nil sets_lemmas nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(pred type-eq-decl nil defined_types nil)
(has_least? const-decl "bool" minmax_orders nil)
(total_order? const-decl "bool" orders nil)
(<= formal-const-decl "(total_order?[T])" total_lattices nil)
(T formal-type-decl nil total_lattices nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" total_lattices nil)
(singleton_has_greatest application-judgement
"(LAMBDA (S: set[T]): has_greatest?(S, <=))" total_lattices nil)
(singleton_has_least application-judgement
"(LAMBDA (S: set[T]): has_least?(S, <=))" total_lattices nil)
(nonempty_union2 application-judgement "(nonempty?)" total_lattices
nil)
(union_preserves_has_least application-judgement
"(LAMBDA (S: set[T]): has_least?(S, <=))" total_lattices nil)
(least_singleton formula-decl nil total_lattices nil)
(singleton const-decl "(singleton?)" sets nil)
(singleton? const-decl "bool" sets nil)
(least_union formula-decl nil total_lattices nil))
shostak)))
¤ Dauer der Verarbeitung: 0.36 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|