proposition: Lemma Rmax_le_compat : forall a b c d, a <= b -> c <= d -> Rmax a c <= Rmax b d.
proof: Proof. intros. unfold Rmax. destruct (Rle_dec a c). destruct (Rle_dec b d). apply H0. apply Rnot_le_lt in n. apply (Rle_trans _ d). apply H0. apply (Rlt_le _ _ n). destruct (Rle_dec b d). apply (Rle_trans _ b). apply H. apply r. apply H. Qed.
imports: Coq(Reals Psatz ssreflect) Coq(ssrbool) mathcomp(seq)