proposition: Lemma slt_cons x y k ks : x <[k :: ks] y = (y != k) && ((x == k) || (x <[ks] y)).
proof: Proof. by rewrite /seq_lt /= !(eq_sym k); case: eqP; case: eqP. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval order) pcm(options prelude ordtype seqext)