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import Mathlib
-- TODO: `even`/`odd` sind in Algebra.Parity. Not ported yet
def even (a : ℕ) : Prop := ∃ r, a = 2 * r
def odd (a : ℕ) : Prop := ∃ k, a = 2 * k + 1
lemma not_odd {n : ℕ} : ¬ odd n ↔ even n := by sorry
lemma not_even {n : ℕ} : ¬ even n ↔ odd n := by sorry
lemma even_square (n : ℕ) : even n → even (n ^ 2) := by