proposition: Lemma fsetDS C A B : A `<=` B -> C `\` B `<=` C `\` A.
proof: Proof. move=> sAB; apply/fsubsetP=> x; rewrite !inE ![_ && (_ \in _)]andbC. by case: (x \in C) => //; apply: contra; exact: (fsubsetP sAB). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrnat eqtype ssrfun seq) mathcomp(choice path finset finfun fintype bigop)