proposition: Lemma slt_rcons_in x y k ks : x \in ks -> x <[rcons ks k] y = x <[ks] y.
proof: Proof. move=>H; rewrite slt_rcons H /=; case: ifP=>// K. by apply/esym; apply: slt_memI=>//; rewrite K. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval order) pcm(options prelude ordtype seqext)