proposition: Lemma Rplus_le_Rmax : forall a b : R, a + b <= 2*Rmax a b.
proof: Proof. intros. rewrite RIneq.double. destruct (Rle_lt_dec a b). rewrite Rmax_right. apply Rplus_le_compat_r. apply r. apply r. rewrite Rmax_left. apply Rplus_le_compat_l. apply Rlt_le. apply r. apply Rlt_le, r. Qed.
imports: Coq(Reals Psatz ssreflect) Coq(ssrbool) mathcomp(seq)