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