(menger
(easy_menger 0
(easy_menger-1 nil 3393145124
("" (skosimp*)
(("" (expand "sep_num")
(("" (lemma "injection_and_cardinal[Path_from(G!1,s!1,t!1),T]")
(("" (inst?)
(("" (assert)
(("" (hide 2)
((""
(case "FORALL (p: (ips!1)):
nonempty?(intersection(min_sep_set(G!1, s!1, t!1),internal_verts(p)))")
(("1" (expand "intersection")
(("1" (expand "member")
(("1"
(inst 1
"(LAMBDA (p: (ips!1)): choose({x: T | min_sep_set[T](G!1, s!1, t!1)(x) AND internal_verts(p)(x)}))")
(("1" (expand "injective?")
(("1" (skosimp*)
(("1" (typepred "x1!1")
(("1" (typepred "x2!1")
(("1"
(expand "path_from?")
(("1"
(flatten)
(("1"
(expand "ind_path_set?")
(("1"
(inst -12 "x1!1" "x2!1")
(("1"
(assert)
(("1"
(expand "independent?")
(("1"
(hide
-1
-2
-3
-4
-5
-6
-7
-8)
(("1"
(typepred
"choose({x: T |
min_sep_set[T](G!1, s!1, t!1)(x) AND internal_verts(x1!1)(x)})")
(("1"
(expand
"internal_verts")
(("1"
(skosimp*)
(("1"
(hide -1)
(("1"
(replace -3 * rl)
(("1"
(hide -3)
(("1"
(typepred
"choose({x: T |
min_sep_set[T](G!1, s!1, t!1)(x) AND internal_verts(x2!1)(x)})")
(("1"
(hide -1)
(("1"
(expand
"internal_verts")
(("1"
(skosimp*)
(("1"
(replace
-3
*
rl)
(("1"
(hide
-3)
(("1"
(expand
"finseq_appl")
(("1"
(inst
-8
"i!1"
"i!2")
(("1"
(assert)
nil)))))))))))))))
("2"
(expand
"nonempty?")
(("2"
(expand
"empty?")
(("2"
(expand
"member")
(("2"
(inst
-4
"x2!1")
(("2"
(skosimp*)
(("2"
(inst?)
(("2"
(assert)
(("2"
(expand
"internal_verts")
(("2"
(expand
"finseq_appl")
(("2"
(inst
+
"i!2")
(("2"
(assert)
nil)))))))))))))))))))))))))))))))))
("2"
(inst -1 "x1!1")
nil)))))))))))))))))))))))))
("2" (skosimp*) (("2" (assert) nil)))))))))
("2" (skosimp*)
(("2" (expand "nonempty?")
(("2" (lemma "min_sep_set_seps")
(("2" (inst?)
(("2" (assert)
(("2" (hide -4 1)
(("2" (expand "separates")
(("2"
(flatten)
(("2"
(inst 3 "p!1")
(("2"
(hide -2 1 2)
(("2"
(typepred "p!1")
(("2"
(expand "path_from?")
(("2"
(flatten)
(("2"
(expand "walk_from?")
(("2"
(expand "from?")
(("2"
(flatten)
(("2"
(assert)
(("2"
(lemma
"walk?_del_verts_not")
(("2"
(inst?)
(("2"
(expand
"path?")
(("2"
(flatten)
(("2"
(assert)
(("2"
(hide
-1
-2
-3
-4
-5
-6
2)
(("2"
(reveal
2
3)
(("2"
(name-replace
"MSS"
"min_sep_set(G!1, s!1, t!1)")
(("2"
(expand
"intersection")
(("2"
(expand
"empty?")
(("2"
(expand
"member")
(("2"
(expand
"verts_of")
(("2"
(expand
"internal_verts")
(("2"
(expand
"finseq_appl")
(("2"
(skosimp*)
(("2"
(inst
-3
"x!1")
(("2"
(assert)
(("2"
(inst?)
(("2"
(assert)
nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
nil)
((sep_num const-decl "nat" sep_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(set_of_paths type-eq-decl nil ind_paths nil)
(min_sep_set const-decl "finite_set[T]" sep_sets nil)
(min_sep_set_seps formula-decl nil sep_sets nil)
(separates const-decl "bool" sep_sets nil)
(from? const-decl "bool" walks nil)
(verts_of const-decl "finite_set[T]" walks nil)
(below type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil) (path? const-decl "bool" paths nil)
(walk?_del_verts_not formula-decl nil sep_sets nil)
(walk_from? const-decl "bool" walks nil)
(G!1 skolem-const-decl "graph[T]" menger nil)
(s!1 skolem-const-decl "T" menger nil)
(t!1 skolem-const-decl "T" menger nil)
(ips!1 skolem-const-decl "set_of_paths[T](G!1, s!1, t!1)" menger
nil)
(choose const-decl "(p)" sets nil)
(independent? const-decl "bool" ind_paths nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props 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)
(empty? const-decl "bool" sets nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(ind_path_set? const-decl "bool" ind_paths nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(injective? const-decl "bool" functions nil)
(member const-decl "bool" sets nil)
(internal_verts const-decl "finite_set[T]" ind_paths nil)
(intersection const-decl "set" sets nil)
(nonempty? const-decl "bool" sets nil)
(finite_intersection1 application-judgement "finite_set"
finite_sets nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(injection_and_cardinal formula-decl nil finite_sets_card_eq
"finite_sets/")
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(below type-eq-decl nil nat_types nil)
(T formal-type-decl nil menger nil)
(finseq type-eq-decl nil finite_sequences 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)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil)
(prewalk type-eq-decl nil walks nil)
(set type-eq-decl nil sets nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(dbl const-decl "set[T]" doubletons nil)
(doubleton type-eq-decl nil doubletons nil)
(finite_set type-eq-decl nil finite_sets nil)
(pregraph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(graph type-eq-decl nil graphs nil)
(path_from? const-decl "bool" paths nil)
(Path_from type-eq-decl nil paths nil))
nil))
(hard_menger 0
(hard_menger-1 nil 3393145124
("" (skosimp*)
(("" (lemma "hard_menger_trad")
(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil)
((T formal-type-decl nil menger nil)
(hard_menger_trad formula-decl nil k_menger 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)
(graph type-eq-decl nil graphs nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pregraph type-eq-decl nil graphs nil)
(finite_set type-eq-decl nil finite_sets nil)
(doubleton type-eq-decl nil doubletons nil)
(dbl const-decl "set[T]" doubletons nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(/= const-decl "boolean" notequal nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil)))
¤ Dauer der Verarbeitung: 0.26 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.
|