proposition: Lemma subsetI A B C : (A \subset B :&: C) = (A \subset B) && (A \subset C).
proof: Proof. rewrite !(sameP setIidPl eqP) setIA; have [-> //|] := eqVneq (A :&: B) A. by apply: contraNF => /eqP <-; rewrite -setIA -setIIl setIAC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)