proposition: Lemma not_Odd_is_Even x : (~Odd x) = Even x.
proof: Proof. apply prop_ext; intro h; generalize (Even_or_Odd x); intros [i|i]. exact i. apply False_rec. exact (h i). destruct h as [k hk]. intro j. destruct j as [l hl]. lia. intros [k hk]. destruct h as [l hl]. lia. Qed.
imports: Coq.Logic.ClassicalEpsilon ClassicalFacts PropExtensionalityFacts Lia PeanoNat