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d03762b | 1 2 3 4 5 6 7 8 9 10 | /- Copyright (c) Heather Macbeth, 2023. All rights reserved. -/
import Library.Theory.Parity
import Library.Theory.ModEq.Defs
theorem Int.odd_iff_modEq (n : ℤ) : Odd n ↔ n ≡ 1 [ZMOD 2] := by
constructor <;> rintro ⟨k, hk⟩ <;> exact ⟨k, by linear_combination hk⟩
theorem Int.even_iff_modEq (n : ℤ) : Even n ↔ n ≡ 0 [ZMOD 2] := by
constructor <;> rintro ⟨k, hk⟩ <;> exact ⟨k, by linear_combination hk⟩
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