proposition: Lemma sle_memE x y ks : x <=[ks] y -> y \in ks -> x \in ks.
proof: Proof. by move=>H; rewrite -!index_mem; apply: leq_ltn_trans H. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval order) pcm(options prelude ordtype seqext)