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import TestGame.Metadata
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import Mathlib.Data.Set.Basic
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Game "TestGame"
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World "SetTheory"
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Level 13
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Title "Konkrete Mengen"
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Introduction
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"
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Um zu überprüfen, dass gewisse Elemente in
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konkreten Mengen enthalten sind, gibt es nicht direkt eine Taktik, aber ein
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einfaches Rezept:
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```
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simp_rw [mem_insert_iff, mem_singleton_iff] at *
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```
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vereinfacht Aussagen der Form `6 ∈ { 0, 6, 1}` zu `(6 = 0) ∨ (6 = 6) ∨ (6 = 1)`,
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und dann kann `tauto` diese Aussage beweisen.
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Bei `⊆` kann man wie schon vorher zuerst mit `intro x hx` die Definition
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auseinandernehmen und dann gleich vorgehen.
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"
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open Set
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Statement
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"" :
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({2, 3, 5} : Set ℕ) ⊆ {4, 2, 5, 7, 3} := by
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intro x hx
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simp_rw [mem_insert_iff, mem_singleton_iff] at *
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tauto
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Tactics simp_rw intro tauto rw
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--Lemmas Subset.antisymm_iff empty_subset
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