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import Mathlib
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
intro ⟨x, hx⟩
unfold Even at *
use 2 * x ^ 2
rw [hx]
ring
theorem nat_succ (n : ℕ) : Nat.succ n = n + 1 := rfl