proposition: Lemma Rplus_lt_le_compat : forall r1 r2 r3 r4, r1 < r2 -> r3 <= r4 -> r1 + r3 < r2 + r4.
proof: Proof. intros r1 r2 r3 r4 Hlt Hle; apply (Rlt_le_trans _ (r2 + r3)). - now apply Rplus_lt_compat_r. - now apply Rplus_le_compat_l. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField