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feat(Algebra/Ring/Parity): Add lemmas Odd.add_one and Odd.one_add (
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IvanRenison committed Nov 21, 2024
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Expand Up @@ -113,6 +113,8 @@ lemma Odd.add_odd : Odd a → Odd b → Even (a + b) := by

@[simp] lemma Even.add_one (h : Even a) : Odd (a + 1) := h.add_odd odd_one
@[simp] lemma Even.one_add (h : Even a) : Odd (1 + a) := h.odd_add odd_one
@[simp] lemma Odd.add_one (h : Odd a) : Even (a + 1) := h.add_odd odd_one
@[simp] lemma Odd.one_add (h : Odd a) : Even (1 + a) := odd_one.add_odd h

lemma odd_two_mul_add_one (a : α) : Odd (2 * a + 1) := ⟨_, rfl⟩

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