proposition: Lemma Rmult_ge_0_gt_0_lt_compat : forall r1 r2 r3 r4, r3 >= 0 -> r2 > 0 -> r1 < r2 -> r3 < r4 -> r1 * r3 < r2 * r4.
proof: Proof. intros r1 r2 r3 r4 H1%Rge_le H2 I J; apply (Rle_lt_trans _ (r2 * r3)). - now apply Rmult_le_compat_r; try apply (Rlt_le r1). - now apply Rmult_lt_compat_l. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField