proposition: Lemma Rplus_le_lt_compat : forall r1 r2 r3 r4, r1 <= r2 -> r3 < r4 -> r1 + r3 < r2 + r4.
proof: Proof. intros r1 r2 r3 r4 H H'; rewrite (Rplus_comm r1), (Rplus_comm r2). now apply Rplus_lt_le_compat. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField