proposition: Lemma ZmaxSS : forall n m : Z, (Zmax n m + 1)%Z = Zmax (n + 1) (m + 1).
proof: Proof. intros. unfold Zmax in |- *. replace (Z.min (n + 1) (m + 1)) with (Z.min n m + 1)%Z. ring. symmetry in |- *. change (Z.min (Z.succ n) (Z.succ m) = Z.succ (Z.min n m)) in |- *. symmetry in |- *. apply Zmin_SS. Qed.
imports: Coq(Lia)