|
(majority_vote
(maj_size 0
(maj_size-1 nil 3286722380
("" (skosimp*)
(("" (use "card_purge_extract")
(("" (replace - :hide? t)
(("" (use "card_extract_bag")
(("" (replace - :hide? t)
(("" (use "minus_add")
(("" (replace - :hide? t)
(("" (use "distributive")
(("" (replace - :hide? t)
(("" (expand ">")
(("" (lemma "both_sides_minus_lt1")
((""
(inst - "(2 * card(A!1)) + (2 * -A!1(v!1))"
"card(A!1)" "(2 * -A!1(v!1))")
(("" (assert) nil))))))))))))))))))))))))
nil)
((card_purge_extract formula-decl nil finite_bags nil)
(T formal-nonempty-type-decl nil majority_vote nil)
(finite_bag type-eq-decl nil finite_bags nil)
(is_finite const-decl "bool" finite_bags nil)
(bag type-eq-decl nil bags 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)
(card_extract_bag formula-decl nil finite_bags nil)
(minus_add formula-decl nil number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(card const-decl "nat" finite_bags nil)
(distributive formula-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(> const-decl "bool" reals 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)
(even_plus_even_is_even application-judgement "even_int" integers
nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(both_sides_minus_lt1 formula-decl nil real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(minus_int_is_int application-judgement "int" integers nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil))
nil))
(maj_single_or_empty 0
(maj_single_or_empty-1 nil 3286722397
("" (skosimp*)
(("" (expand "empty?")
(("" (skosimp*)
(("" (expand "member")
(("" (expand "maj?")
(("" (expand "singleton?")
(("" (inst?)
(("" (skosimp*)
(("" (typepred! "y!1")
(("" (lemma "card_geq_count_add")
(("" (inst - "A!1" "x!1" "y!1")
(("" (assert) nil))))))))))))))))))))))
nil)
((empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil)
(singleton? const-decl "bool" sets nil)
(card_geq_count_add formula-decl nil finite_bags nil)
(NOT const-decl "[bool -> bool]" booleans 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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(T formal-nonempty-type-decl nil majority_vote 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)
(bag type-eq-decl nil bags nil)
(is_finite const-decl "bool" finite_bags nil)
(finite_bag type-eq-decl nil finite_bags nil)
(A!1 skolem-const-decl "finite_bag[T]" majority_vote nil)
(x!1 skolem-const-decl "T" majority_vote nil)
(card const-decl "nat" finite_bags 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)
(maj? const-decl "bool" majority_vote nil))
nil))
(maj_unique 0
(maj_unique-1 nil 3286722448
("" (skosimp*)
(("" (expand "maj")
(("" (lift-if)
(("" (split)
(("1" (flatten) (("1" (grind) nil nil)) nil)
("2" (flatten)
(("2" (use "maj_single_or_empty")
(("2" (split)
(("1" (case "singleton(v!1) = maj?(A!1)")
(("1" (use "choose_singleton")
(("1" (lemma "choose_is_epsilon[T]")
(("1" (inst?) (("1" (replace*) nil nil)) nil))
nil))
nil)
("2" (expand "singleton?")
(("2" (skosimp*)
(("2" (inst-cp - "epsilon(maj?(A!1))")
(("1" (inst - "v!1") (("1" (replace*) nil nil))
nil)
("2" (use "epsilon_ax[T]")
(("2" (split)
(("1" (propax) nil nil)
("2" (inst + "v!1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((maj const-decl "T" majority_vote nil)
(nil application-judgement "nat" majority_vote nil)
(nil application-judgement "nonneg_real" majority_vote 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)
(nil application-judgement "finite_set" majority_vote nil)
(T formal-nonempty-type-decl nil majority_vote nil)
(bag_to_set const-decl "set[T]" bags_to_sets nil)
(member const-decl "bool" sets nil)
(empty? const-decl "bool" sets nil)
(card const-decl "nat" finite_bags nil)
(maj? const-decl "bool" majority_vote nil)
(maj_single_or_empty formula-decl nil majority_vote nil)
(finite_bag type-eq-decl nil finite_bags nil)
(is_finite const-decl "bool" finite_bags nil)
(bag type-eq-decl nil bags 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)
(singleton const-decl "(singleton?)" sets nil)
(singleton? const-decl "bool" sets nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(set type-eq-decl nil sets nil)
(nonempty_singleton_finite application-judgement
"non_empty_finite_set[T]" majority_vote nil)
(choose_is_epsilon formula-decl nil sets nil)
(nonempty? const-decl "bool" sets nil)
(choose_singleton formula-decl nil sets_lemmas nil)
(epsilon_ax formula-decl nil epsilons nil)
(v!1 skolem-const-decl "T" majority_vote nil)
(epsilon const-decl "T" epsilons nil)
(pred type-eq-decl nil defined_types nil)
(A!1 skolem-const-decl "finite_bag[T]" majority_vote nil))
nil))
(maj_pigeonhole 0
(maj_pigeonhole-1 nil 3286906485
("" (skosimp*)
(("" (lemma "maj_unique")
(("" (inst - "A!1" _)
(("" (inst-cp - "v!1")
(("" (inst - "i!1") (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
((maj_unique formula-decl nil majority_vote nil)
(finite_bag type-eq-decl nil finite_bags nil)
(is_finite const-decl "bool" finite_bags nil)
(bag type-eq-decl nil bags 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_vote nil))
shostak))
(maj_is_extraction 0
(maj_is_extraction-1 nil 3286722458
("" (skosimp*)
(("" (decompose-equality +)
(("" (expand "maj?")
(("" (iff)
(("" (prop)
(("1" (expand "bag_to_set")
(("1" (expand "extract")
(("1" (lift-if)
(("1" (split)
(("1" (flatten) (("1" (assert) nil)))
("2" (flatten)
(("2" (lemma "card_geq_count_add")
(("2" (inst - "A!1" "x!1" "v!1")
(("2" (assert) nil)))))))))))))))
("2" (expand "bag_to_set")
(("2" (expand "extract")
(("2" (lift-if)
(("2" (split)
(("1" (flatten)
(("1" (replace -) (("1" (propax) nil)))))
("2" (flatten)
(("2" (assert) nil))))))))))))))))))))
nil)
((nil application-judgement "finite_bag[T]" majority_vote nil)
(nil application-judgement "finite_set" majority_vote 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)
(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)
(maj? const-decl "bool" majority_vote nil)
(set type-eq-decl nil sets nil)
(bag_to_set const-decl "set[T]" bags_to_sets nil)
(extract const-decl "bag" bags nil)
(boolean nonempty-type-decl nil booleans nil)
(T formal-nonempty-type-decl nil majority_vote nil)
(card_geq_count_add formula-decl nil finite_bags 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))
nil)))
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