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