proposition: Lemma setUIl A B C : (A :&: B) :|: C = (A :|: C) :&: (B :|: C).
proof: Proof. by apply/setP=> x; rewrite !inE orb_andl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)