proposition: Lemma lt_creal_trans (x y z : creal) : (x < y -> y < z -> x < z)%CR.
proof: Proof. move=> lt_xy lt_yz; pose_big_enough i. apply: (@lt_crealP (diff lt_xy + diff lt_yz) i i) => //. by rewrite addr_gt0 ?diff_gt0. rewrite (le_trans _ (diff_of lt_yz)) //. by rewrite addrA ler_add2r (diff_of lt_xy). by close. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrnum ssrint rat poly polydiv polyorder) mathcomp(perm matrix mxpoly polyXY binomial bigenough)