|
(middle_value_select
(mid_val_singleton 0
(mid_val_singleton-1 nil 3287920647
("" (skosimp*)
(("" (expand "singleton?")
(("" (inst + "epsilon(mid_val?(A!1))")
(("1" (skosimp*)
(("1" (typepred! "y!1")
(("1" (expand "mid_val?")
(("1" (flatten)
(("1"
(name-replace "xx" "epsilon(LAMBDA (v):
2 * card(l_filter(A!1, v)) > card(A!1) AND
2 * card(u_filter(A!1, v)) >= card(A!1))")
(("1" (lemma "maj_pigeonhole")
(("1"
(inst-cp - "l_filter(A!1, y!1)"
"u_filter(A!1, xx)" "A!1")
(("1"
(inst - "l_filter(A!1, xx)"
"u_filter(A!1, y!1)" "A!1")
(("1" (expand "member")
(("1" (typepred! "leq")
(("1" (expand "total_order?")
(("1"
(expand "partial_order?")
(("1"
(expand "preorder?")
(("1"
(flatten)
(("1"
(assert)
(("1"
(split)
(("1"
(skosimp*)
(("1"
(split)
(("1"
(skosimp*)
(("1"
(grind)
(("1"
(reveal -4)
(("1"
(inst
-
"y!1"
"x!1"
"xx")
(("1"
(assert)
nil
nil))
nil))
nil)
("2"
(reveal -4)
(("2"
(inst
-
"xx"
"x!2"
"y!1")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil)
("2"
(use "l_filter_subbag")
nil
nil)
("3"
(hide-all-but (2 1))
(("3"
(expand "xx")
(("3"
(use "epsilon_ax[T]")
(("3"
(split)
(("1"
(flatten)
nil
nil)
("2"
(hide 2)
(("2"
(use
"filter_exists")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4"
(use "u_filter_subbag")
nil
nil))
nil))
nil)
("2"
(split)
(("1"
(skosimp*)
(("1"
(hide-all-but (1 2))
(("1"
(expand "xx")
(("1"
(use "epsilon_ax[T]")
(("1"
(split)
(("1"
(flatten)
nil
nil)
("2"
(hide 2)
(("2"
(use
"filter_exists")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(use "l_filter_subbag")
nil
nil)
("3"
(hide-all-but (1 3))
(("3"
(expand "xx")
(("3"
(use "epsilon_ax[T]")
(("3"
(split)
(("1"
(flatten)
nil
nil)
("2"
(hide 2)
(("2"
(use
"filter_exists")
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("4"
(use "u_filter_subbag")
nil
nil))
nil)
("3"
(use "l_filter_subbag")
nil
nil)
("4"
(use "u_filter_subbag")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (use "epsilon_ax[T]")
(("2" (split)
(("1" (propax) nil nil)
("2" (hide 2)
(("2" (expand "mid_val?")
(("2" (use "filter_exists") (("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((singleton? const-decl "bool" sets nil)
(nil application-judgement "finite_bag[T]" middle_value_select nil)
(nil application-judgement "finite_bag[T]" middle_value_select nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(> const-decl "bool" reals nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(card const-decl "nat" finite_bags nil)
(total_order? const-decl "bool" orders nil)
(leq formal-const-decl "(total_order?[T])" middle_value_select nil)
(l_filter const-decl "bag" bag_filters nil)
(u_filter const-decl "bag" bag_filters nil)
(member const-decl "bool" bags nil)
(preorder? const-decl "bool" orders nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(u_filter_subbag formula-decl nil bag_filters nil)
(epsilon_ax formula-decl nil epsilons nil)
(filter_exists formula-decl nil bag_filters nil)
(xx skolem-const-decl "T" middle_value_select nil)
(l_filter_subbag formula-decl nil bag_filters nil)
(nil application-judgement "finite_set" middle_value_select nil)
(nil application-judgement "nat" middle_value_select nil)
(nil application-judgement "int" middle_value_select nil)
(reflexive? const-decl "bool" relations nil)
(transitive? const-decl "bool" relations nil)
(antisymmetric? const-decl "bool" relations nil)
(dichotomous? const-decl "bool" orders nil)
(bag_to_set const-decl "set[T]" bags_to_sets nil)
(member const-decl "bool" sets nil)
(empty? const-decl "bool" sets nil)
(empty? const-decl "bool" bags nil)
(partial_order? const-decl "bool" orders nil)
(maj_pigeonhole formula-decl nil bag_filters nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(T formal-nonempty-type-decl nil middle_value_select 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)
(bag type-eq-decl nil bags nil)
(is_finite const-decl "bool" finite_bags nil)
(finite_bag type-eq-decl nil finite_bags nil)
(mid_val? const-decl "bool" middle_value_select nil)
(A!1 skolem-const-decl "finite_bag[T]" middle_value_select nil)
(pred type-eq-decl nil defined_types nil)
(epsilon const-decl "T" epsilons nil))
shostak)))
¤ Dauer der Verarbeitung: 0.6 Sekunden
(vorverarbeitet)
¤
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