proposition: Lemma slt_sortedE ks x y : sorted ord ks -> x \in ks -> y \in ks -> x <[ks] y = ord x y.
proof: Proof. move=>S X Y; apply/idP/idP; first by apply: slt_sorted S Y. by apply: (sorted_ord_index (@irr _) (@trans _)) S X. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval order) pcm(options prelude ordtype seqext)