(middle_third_overlapnil 3414576950"" (skosimp*)"" (rewrite "min_reduce" )"" (rewrite "max_reduce" )"" (lemma "middle_third_pigeonhole[N]" )"" "highset(v1!1, e1!1, byz(card(e1!1)))" "lowset(v2!1, e2!1, card(e2!1) - 1 - byz(card(e2!1)))" "src_set!1" "e1!1" "e2!1" )"" (prop)"1" (expand * "highset" "lowset" )"1" (skosimp*)"1" (inst?) (("1" (prop) nil nil )) nil )) nil ))nil )"2" (use "card_highset" )"2" (expand * "two_thirds_majority_subset?" "byz" )"2" (assert )"2" (expand * "subset?" "highset" "member" )"2" (skosimp*) nil nil )) nil ))nil ))nil ))nil )"3" (use "card_lowset" )"3" (expand * "two_thirds_majority_subset?" "byz" )"3" (assert )"3" (expand * "subset?" "lowset" "member" )"3" (skosimp*) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil reduce_properties nil )nil naturalnumbers nil )"bool" reals nil )nil naturalnumbers nil )set type-eq-decl nil sets nil )"bool" finite_sets nil )nil finite_sets nil )NOT const-decl "[bool -> bool]" booleans nil )"bool" sets nil )nil finite_sets nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil tau_declaration nil )"tau_type" tau_declaration nil )nil node nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil integers nil )"bool" reals nil )nil integers nil )"posnat" middle_third_overlap nil )nil middle_third_overlap nil )nil defined_types nil )"bool" orders nil )"(total_order?[T])" middle_third_overlap nil )"ne_seqs[T]" nil )nil middle_third_pigeonholenil )"nat" floor_ceil nil )"bool" pigeonhole nil )"bool" sets nil )"bool" sets nil )"(total_order?[real])" nil )"nonneg_rat" nil )"nonneg_int" nil )"(divides(n))" divides nil )"(divides(m))" divides nil )"even_int" integersnil )nil reduce_properties nil )nil reduce_properties nil )"[T, T -> boolean]" equalities nil )"nat" finite_sets nil )"{n: nat | n = Card(S)}" finite_sets nil )"finite_set[below(N)]" reduce_properties nil )"finite_set[below(N)]" reduce_properties nil )"[numfield, numfield -> numfield]" number_fields nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"int" integers nil )nil reduce_properties nil ))nil )nil 3403897718"" (skosimp*)"" (rewrite "min_reduce" )"" (rewrite "max_reduce" )"" (lemma "middle_third_pigeonhole[N]" )"" "highset(e1!1, f1!1, byz(card(e1!1)))" "lowset(e2!1, f2!1, card(e2!1) - 1 - byz(card(e2!1)))" "src_set!1" "e1!1" "e2!1" )"" (prop)"1" (expand * "highset" "lowset" )"1" (skosimp*)"1" (inst?) (("1" (prop) nil nil )) nil )) nil ))nil )"2" (use "card_highset" )"2" (expand * "two_thirds_majority_subset?" "byz" )"2" (assert )"2" (expand * "subset?" "highset" "member" )"2" (skosimp*) nil nil )) nil ))nil ))nil ))nil )"3" (use "card_lowset" )"3" (expand * "two_thirds_majority_subset?" "byz" )"3" (assert )"3" (expand * "subset?" "lowset" "member" )"3" (skosimp*) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil reduce_properties nil )nil node nil )nil tau_declaration nil )"tau_type" tau_declaration nil )"bool" orders nil )nil middle_third_pigeonholenil )"bool" pigeonhole nil )nil reduce_properties nil )nil reduce_properties nil )"finite_set[below(N)]" reduce_properties nil )"finite_set[below(N)]" reduce_properties nil )nil reduce_properties nil ))nil )nil 3398091778"" (skosimp*)"" (rewrite "min_reduce" )"" (rewrite "max_reduce" )"" (typepred "index(enabled1!1, f1!1)(byz(enabled1!1))" )"" "index(enabled2!1, f2!1)(card[below(N)](enabled2!1) - 1 - byz(enabled2!1))" )"" (expand "index_value" )"" (flatten)"" (hide -1 -2 -4 -5 -6 -7)"" (expand "byz" )"" (lemma "middle_third_pigeonhole[N]" )"" "%1" "%2" _ _ _) (! -3 l 1)"1" (inst?)"1" (expand "two_thirds_majority_subset?" )"1" (rewrite "subset_filter" )"1" rewrite "subset_filter" )"1" assert )"1" "1" "1" expand "filter" )"1" expand ">=" )"1" "1" "1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"bool" orders nil )nil middle_third_pigeonholenil )"bool" pigeonhole nil ))nil )nil 3377615981"" (skosimp*)"" (rewrite "min_reduce" )"" (rewrite "max_reduce" )"" (typepred "index(eligible1!1, f1!1)(tau(eligible1!1))" )"" "index(eligible2!1, f2!1) ") "" (expand "index_value" )"" (flatten)"" (hide -1 -2 -4 -5 -6 -7)"" (expand "tau" )"" (lemma "middle_third_pigeonhole[N]" )"" "%1" "%2" _ _ _) (! -3 l 1)"1" (inst?)"1" (expand "two_thirds_majority_subset?" )"1" (rewrite "subset_filter" )"1" rewrite "subset_filter" )"1" assert )"1" "1" "1" expand "filter" )"1" expand ">=" )"1" "1" "1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"bool" orders nil )nil middle_third_pigeonholenil )"bool" pigeonhole nil ))nil )))quality 100%
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