proposition: Lemma Zge_gt_plus_plus : forall m n p q : Z, (m >= n)%Z -> (p > q)%Z -> (m + p > n + q)%Z.
proof: Proof. intros. case (Zle_lt_or_eq n m). apply Z.ge_le. assumption. intro. apply Zgt_plus_plus. apply Z.lt_gt. assumption. assumption. intro. rewrite H1. apply Zplus_gt_compat_l. assumption. Qed.
imports: Coq(Lia)