proposition: Lemma Rmax_Rle : forall r1 r2 r, r <= Rmax r1 r2 <-> r <= r1 \/ r <= r2.
proof: Proof. intros; split. - unfold Rmax; case (Rle_dec r1 r2); intros; auto. - intro; unfold Rmax; case (Rle_dec r1 r2) as [|Hnle]; elim H; clear H; intros; auto. + apply (Rle_trans r r1 r2); auto. + generalize (Rnot_le_lt r1 r2 Hnle); clear Hnle; intro; unfold Rgt in H0; apply (Rlt_le r r1 (Rle_lt_trans r r2 r1 H H0)). Qed.
imports: Rdefinitions Raxioms RIneq R_Ifp