proposition: Lemma Rdist_pos : forall x y:R, Rdist x y >= 0.
proof: Proof. intros; unfold Rdist; unfold Rabs; case (Rcase_abs (x - y)); intro l. - unfold Rge; left; apply (Ropp_gt_lt_0_contravar (x - y) l). - trivial. Qed.
imports: ArithRing Rdefinitions Raxioms RIneq Rpow_def R_Ifp Rbasic_fun R_sqr SplitAbsolu SplitRmult ArithProp Zpower Ztac