proposition: Theorem add_max_distr_r : ∀ n m p, max (n + p) (m + p) = max n m + p.
proof: Proof. intros n m p. destruct n as [n| ]; [ simpl | reflexivity ]. destruct p as [p| ]; [ simpl | destruct m; reflexivity ]. destruct m; [ simpl | reflexivity ]. rewrite Nat.add_max_distr_r; reflexivity. Qed.
imports: Utf8 Compare_dec NPeano Misc