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(majority_array
(is_majority_TCC1 0
(is_majority_TCC1-1 nil 3506271671
("" (skosimp*) (("" (rewrite "finite_below") nil)) nil)
((finite_below formula-decl nil finite_sets_below "finite_sets/")
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil)
(below type-eq-decl nil naturalnumbers nil)
(set type-eq-decl nil sets nil)
(below type-eq-decl nil nat_types nil)
(T formal-nonempty-type-decl nil majority_array nil)
(= const-decl "[T, T -> boolean]" equalities 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)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "posnat" majority_array nil))
nil))
(maj_TCC1 0
(maj_TCC1-1 nil 3506271671
(""
(inst 1 "(LAMBDA A:
IF maj_exists(A) THEN
choose({mv: T | is_majority(mv, A)})
ELSE
epsilon({mv: T | TRUE})
ENDIF)")
(("1" (skosimp*) nil) ("2" (skosimp*) (("2" (assert) nil)))
("3" (grind) nil))
nil)
((member const-decl "bool" sets nil)
(empty? const-decl "bool" sets nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(TRUE const-decl "bool" booleans nil)
(epsilon const-decl "T" epsilons nil)
(pred type-eq-decl nil defined_types nil)
(choose const-decl "(p)" sets nil)
(nonempty? const-decl "bool" sets nil)
(set type-eq-decl nil sets nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(is_majority const-decl "bool" majority_array nil)
(maj_exists const-decl "bool" majority_array nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(T formal-nonempty-type-decl nil majority_array nil)
(below type-eq-decl nil nat_types nil)
(N formal-const-decl "posnat" majority_array nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(< const-decl "bool" reals 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))
nil))
(is_majority_unique 0
(is_majority_unique-1 nil 3506271671
("" (skosimp*)
(("" (expand "is_majority")
((""
(case "disjoint?({ii | A!1(ii) = mv1!1},{ii | A!1(ii) = mv2!1})")
(("1" (lemma "card_disj_union[below(N)]")
(("1" (inst?)
(("1" (assert)
(("1" (hide -2)
(("1"
(case "card(union({ii | A!1(ii) = mv1!1}, {ii | A!1(ii) = mv2!1})) <= N")
(("1" (replace -2)
(("1" (hide -2 -3 -4 1) (("1" (assert) nil)))))
("2" (hide -1 -2 -3)
(("2" (rewrite "card_below") nil)))
("3" (rewrite "finite_below") nil)))))))
("2" (rewrite "finite_below") nil)
("3" (rewrite "finite_below") nil)))))
("2" (expand "disjoint?")
(("2" (expand "intersection")
(("2" (expand "empty?")
(("2" (expand "member")
(("2" (skosimp*) (("2" (assert) nil))))))))))))))))
nil)
((is_majority const-decl "bool" majority_array nil)
(empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(intersection const-decl "set" sets nil)
(card_disj_union formula-decl nil finite_sets nil)
(below type-eq-decl nil naturalnumbers nil)
(finite_below formula-decl nil finite_sets_below "finite_sets/")
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(<= const-decl "bool" reals nil)
(Card const-decl "nat" finite_sets nil)
(card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
(union const-decl "set" sets nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(card_below formula-decl nil finite_sets_below "finite_sets/")
(finite_set type-eq-decl nil finite_sets nil)
(mv2!1 skolem-const-decl "T" majority_array nil)
(is_finite const-decl "bool" finite_sets nil)
(A!1 skolem-const-decl "[below[N] -> T]" majority_array nil)
(mv1!1 skolem-const-decl "T" majority_array 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)
(< const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "posnat" majority_array nil)
(below type-eq-decl nil nat_types nil)
(set type-eq-decl nil sets nil)
(disjoint? const-decl "bool" sets nil)
(T formal-nonempty-type-decl nil majority_array nil)
(= const-decl "[T, T -> boolean]" equalities nil))
nil))
(maj_lem 0
(maj_lem-1 nil 3506271671
("" (skosimp*)
(("" (prop)
(("1" (expand "maj_exists") (("1" (inst?) nil)))
("2" (typepred "maj(A!1)")
(("2" (split -1)
(("1" (lemma "is_majority_unique")
(("1" (inst -1 "A!1" "mv!1" "maj(A!1)")
(("1" (assert) nil)))))
("2" (expand "maj_exists") (("2" (inst?) nil)))))))
("3" (typepred "maj(A!1)") (("3" (assert) nil))))))
nil)
((T formal-nonempty-type-decl nil majority_array nil)
(maj_exists const-decl "bool" majority_array nil)
(is_majority_unique formula-decl nil majority_array nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(IMPLIES const-decl "[bool, 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)
(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)
(< const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "posnat" majority_array nil)
(below type-eq-decl nil nat_types nil)
(is_majority const-decl "bool" majority_array nil)
(maj const-decl "{mv | maj_exists(A) => is_majority(mv, A)}"
majority_array nil))
nil))
(maj_subset 0
(maj_subset-1 nil 3506271671
("" (skosimp*)
(("" (expand "is_majority")
(("" (case "subset?(IDS!1,{ii | A!1(ii) = mv!1})")
(("1" (lemma "card_subset[below(N)]")
(("1" (inst?)
(("1" (assert) nil) ("2" (rewrite "finite_below") nil)))))
("2" (hide -1 2)
(("2" (expand "subset?")
(("2" (skosimp*)
(("2" (expand "member")
(("2" (inst -2 "x!1")
(("2" (assert) nil))))))))))))))))
nil)
((is_majority const-decl "bool" majority_array nil)
(member const-decl "bool" sets nil)
(card_subset formula-decl nil finite_sets nil)
(finite_below formula-decl nil finite_sets_below "finite_sets/")
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil)
(mv!1 skolem-const-decl "T" majority_array nil)
(A!1 skolem-const-decl "[below[N] -> T]" majority_array 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)
(< const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "posnat" majority_array nil)
(below type-eq-decl nil naturalnumbers nil)
(set type-eq-decl nil sets nil)
(subset? const-decl "bool" sets nil)
(is_finite const-decl "bool" finite_sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(below type-eq-decl nil nat_types nil)
(T formal-nonempty-type-decl nil majority_array nil)
(= const-decl "[T, T -> boolean]" equalities nil))
nil))
(maj_in_array 0
(maj_in_array-1 nil 3506271671
("" (skosimp*)
(("" (expand "is_majority")
(("" (lemma "card_empty?[below(N)]")
(("" (inst?)
(("1" (expand "empty?")
(("1" (expand "member")
(("1" (iff -1)
(("1" (flatten)
(("1" (split -1)
(("1" (assert) nil)
("2" (split -1)
(("1" (propax) nil)
("2" (skosimp*) (("2" (inst?) nil)))))))))))))))
("2" (rewrite "finite_below") nil))))))))
nil)
((is_majority const-decl "bool" majority_array nil)
(mv!1 skolem-const-decl "T" majority_array nil)
(A!1 skolem-const-decl "[below[N] -> T]" majority_array nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(T formal-nonempty-type-decl nil majority_array nil)
(below type-eq-decl nil nat_types nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(finite_set type-eq-decl nil finite_sets nil)
(member const-decl "bool" sets nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(empty? const-decl "bool" sets nil)
(finite_below formula-decl nil finite_sets_below "finite_sets/")
(card_empty? formula-decl nil finite_sets 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)
(< const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(N formal-const-decl "posnat" majority_array nil)
(below type-eq-decl nil naturalnumbers nil))
nil))
(is_majority_const 0
(is_majority_const-1 nil 3506271671
("" (skosimp*)
(("" (lemma "card_below_fullset")
(("" (expand "constant_array")
(("" (expand "is_majority")
(("" (expand "fullset") (("" (assert) nil))))))))))
nil)
((N formal-const-decl "posnat" majority_array nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers 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)
(card_below_fullset formula-decl nil finite_sets_below
"finite_sets/")
(is_majority const-decl "bool" majority_array nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fullset const-decl "set" sets nil)
(constant_array const-decl "below_array" majority_array nil))
nil))
(maj_const 0
(maj_const-1 nil 3506271671
("" (skosimp*)
(("" (lemma "is_majority_const")
(("" (inst?)
(("" (lemma "maj_lem") (("" (inst?) (("" (ground) nil))))))))))
nil)
((is_majority_const formula-decl nil majority_array nil)
(maj_lem formula-decl nil majority_array nil)
(constant_array const-decl "below_array" majority_array nil)
(below_array type-eq-decl nil below_arrays nil)
(below type-eq-decl nil naturalnumbers nil)
(below type-eq-decl nil nat_types nil)
(N formal-const-decl "posnat" majority_array nil)
(posnat nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(< const-decl "bool" reals 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)
(T formal-nonempty-type-decl nil majority_array nil))
nil)))
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