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