proposition: Lemma Rinv_0_lt_contravar : forall r1 r2, 0 < r1 -> r1 < r2 -> / r2 < / r1.
proof: Proof. intros r1 r2 H1 I. assert (H2 : 0 < r2) by now apply (Rlt_trans _ r1). apply (Rmult_lt_reg_l r2); try easy. rewrite Rinv_r by now apply Rgt_not_eq. apply (Rmult_lt_reg_r r1); try easy. rewrite Rmult_assoc, Rinv_l by now apply Rgt_not_eq. now rewrite Rmult_1_r, Rmult_1_l. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField