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