{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-subset"},"kind":"guides","total":2,"pages":1,"page":1,"entries":[{"id":"derivation-mko-subset-01","title":{"zh-Hant":"子集合：以任意元素證明包含，並以反例否定包含","en":"Subset: proving inclusion from an arbitrary element and refuting it by a counterexample"},"summary":{"zh-Hant":"在論域 ℤ 中，令 A 為 6 的倍數之集、B 為偶數之集、C 為 4 的倍數之集。證明 A⊆B，且這個包含是嚴格的（A≠B）；證明 A⊄C，雖然 A 與 C 有共同元素 12；說明 B⊆B 成立（⊆ 允許相等）；並證明 {6}⊆A ⇔ 6∈A，同時分辨兩個語句的型別角色。","en":"In the universe ℤ, let A be the set of multiples of 6, B the set of even integers and C the set of multiples of 4. Prove A⊆B and that this inclusion is strict (A≠B); prove A⊄C even though A and C share the element 12; note that B⊆B holds (⊆ allows equality); and prove {6}⊆A ⇔ 6∈A while separating the type roles of the two statements."},"mko_ids":["mko-subset"]},{"id":"derivation-mko-subset-construction-nfa-to-dfa-01","title":{"zh-Hant":"epsilon-NFA的完整reachable subset DFA","en":"The complete reachable-subset DFA of an epsilon-NFA"},"summary":{"zh-Hant":"完整列轉移並以prefix induction證語言等價。","en":"List every transition and prove language equivalence by prefix induction."},"mko_ids":["mko-subset-construction-nfa-to-dfa"]}],"title":"概念推導導讀"}