proposition: Lemma properIl A B : ~~ (A \subset B) -> A :&: B \proper A.
proof: Proof. by move=> nsBA; rewrite properE subsetIl subsetI negb_and nsBA orbT. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)