proposition: Lemma sle_eqVlt ks t1 t2 : (t1 \in ks) || (t2 \in ks) -> t1 <=[ks] t2 = (t1 == t2) || (t1 <[ks] t2).
proof: Proof. move=>H; rewrite /seq_lt /seq_le leq_eqVlt /=. case: (t1 =P t2)=>[->|N] /=; first by rewrite eq_refl. case: eqP=>//=; case/orP: H=>H; first by move/(index_inj H)/N. by move/esym/(index_inj H)/esym/N. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path interval order) pcm(options prelude ordtype seqext)