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import TestGame.Metadata
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import Mathlib.Data.Set.Basic
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import Mathlib.Algebra.Parity
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import Mathlib
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Game "TestGame"
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World "SetTheory2"
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Level 4
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Title ""
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Introduction
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"
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"
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open Set
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Statement
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"" :
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{2, 7} ⊆ {n : ℕ | n = 2 ∨ (n ≤ 10 ∧ Odd n)} := by
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rw [setOf_or, setOf_and]
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intro x hx
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rw [mem_union, mem_inter_iff]
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simp_rw [mem_setOf, mem_insert_iff, mem_singleton_iff] at *
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rcases hx with hx | hx
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left
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assumption
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right
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constructor
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linarith
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use 3
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rw [hx]
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ring
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Tactics constructor intro rw assumption rcases simp tauto trivial
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Lemmas Subset.antisymm_iff empty_subset
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