proposition: Lemma subset_cat2 s1 s2 s3 : s1 \subset s2 -> s3 ++ s1 \subset s3 ++ s2.
proof: Proof. move=> /subsetP s12; apply/subsetP => x. by rewrite !mem_cat => /orP[->|/s12->]; rewrite ?orbT. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)