(finite_cyclic_groupsnil 3408118121"" (rewrite "fullset_is_group" ) nil nil )nil finite_cyclic_groups nil )) nil ))nil 3407853657"" (skosimp*)"" (expand "cyclic?" )"" (expand "order" )"" (case "card(G!1) > 1" )"1" (case "(EXISTS (a: (G!1)): a /= one)" )"1" (skosimp*)"1" (name "HH" "generated_by(a!1)" )"1" (inst + "a!1" )"1" (assert )"1" (replace -1)"1" (case "subgroup?(HH,G!1)" )"1" (lemma "Lagrange" )"1" (inst?)"1" (assert )"1" expand "prime?" )"1" "order(HH)" )"1" expand "order" )"1" "1" (propax) nil nil )"2" assert )"2" "2" "generated_by_card_1" )"2" "2" "G!1" )"2" expand "member" )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" "3" assert )"3" "3" expand "subgroup?" )"3" "same_card_subset[T]" )"3" "HH" "G!1" )"3" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (typepred "G!1" )"2" "finite_subgroups" )"2" "2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "generated_is_subgroup" )"2" (inst?)"2" (inst - "G!1" )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide -2 2)"2" (lemma "card_2_has_2[T]" )"2" (inst - "G!1" )"2" (assert )"2" (skosimp*)"2" (inst-cp + "x!1" )"2" (inst + "y!1" ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "prime?" ) (("2" (flatten) nil nil )) nil ))nil ))nil ))nil ))nil )"boolean" group nil )nil group nil )"bool" group_def nil )"T" finite_cyclic_groups nil )"[T, T -> T]" finite_cyclic_groups nil )"{n: nat | n = Card(S)}" finite_sets nil )"nat" finite_sets nil )"[T, T -> boolean]" equalities nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil finite_sets nil )"bool" finite_sets nil )set type-eq-decl nil sets nil )nil finite_cyclic_groups nil )"bool" reals nil )nil booleans nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"T" finite_cyclic_groups nil )"T" finite_cyclic_groups nil )"finite_group[T, *, one]" nil )"(total_order?[real])" nil )nil finite_sets nil )nil cyclic_group nil )nil lagrange nil )NOT const-decl "[bool -> bool]" booleans nil )nil group nil )nil monad nil )"bool" monad_def nil )nil integers nil )nil integers nil )"bool" sets nil )nil finite_groups nil )"(partial_order?[set[T]])" nil )nil finite_sets nil )"bool" primes "ints/" )"group[T, *, one]" finite_cyclic_groups nil )"bool" group_def nil )"(strict_total_order?[real])" real_props nil )"group" group nil )nil group nil )"bool" group_def nil )"boolean" notequal nil )"posnat" monad nil ))nil )nil 3407082460";;; Proof prime_order_cycle-3 for formula finite_cyclic_groups.prime_order_cycle" ";;; Proof prime_order_cycle-3 for formula finite_cyclic_groups.prime_order_cycle" expand "cyclic?" )";;; Proof prime_order_cycle-3 for formula finite_cyclic_groups.prime_order_cycle" expand "order" )";;; Proof prime_order_cycle-3 for formula finite_cyclic_groups.prime_order_cycle" case "card(G!1) > 1" )"1" (case "(EXISTS (a: (G!1)): a /= one)" )"1" (skosimp*)"1" (name "HH" "generated_by(a!1)" )"1" (inst + "a!1" )"1" (assert )"1" (replace -1)"1" (case "subgroup?(HH,G!1)" )"1" (lemma "Lagrange" )"1" (inst?)"1" (assert )"1" expand "prime?" )"1" "order(HH)" )"1" expand "order" )"1" assert )"1" "1" assert )"1" expand "divides" )"1" (propax) nil )))))"2" "2" "generated_by_card_1" )"2" "2" "G!1" )"2" expand "member" )"2" assert )nil )))))))))))"3" "3" assert )"3" "3" expand "subgroup?" )"3" "same_card_subset[T]" )"3" "HH" "G!1" )"3" assert )nil )))))))))))))))))))))))))"2" (typepred "G!1" )"2" "finite_subgroups" )"2" "2" (assert ) nil )))))))))))"2" (lemma "generated_is_subgroup" )"2" (inst?)"2" (inst - "G!1" )"2" (assert ) nil )))))))))))))))))))"2" (hide -2 2)"2" (lemma "card_2_has_2[T]" )"2" (inst - "G!1" )"2" (assert )"2" (skosimp*)"2" (inst-cp + "x!1" )"2" (inst + "y!1" )"2" (assert ) nil )))))))))))))))))"2" (expand "prime?" ) (("2" (flatten) nil ))))))))))";;; developed with shostak decision procedures") "boolean" group nil )nil group nil )"bool" group_def nil )nil group nil )nil lagrange nil )nil group nil )nil monad nil )"bool" monad_def nil )"bool" group_def nil )"group" group nil )nil group nil )"bool" group_def nil )"posnat" monad nil ))nil )))quality 86%
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