proposition: Lemma cover_setI P D : cover (P ::&: D) \subset cover P :&: D.
proof: Proof. by apply/bigcupsP=> A /setIdP[PA sAD]; rewrite subsetI sAD andbT (bigcup_max A). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)