proposition: Lemma Rmult_le_compat : forall r1 r2 r3 r4, 0 <= r1 -> 0 <= r3 -> r1 <= r2 -> r3 <= r4 -> r1 * r3 <= r2 * r4.
proof: Proof. intros r1 r2 r3 r4 H1 H2 I J; apply (Rle_trans _ (r2 * r3)). - now apply Rmult_le_compat_r. - assert (H3 : 0 <= r2) by now apply (Rle_trans _ r1). now apply Rmult_le_compat_l. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField