proposition: Lemma tuto_setUIl : forall A B C, (A :&: B) :|: C = (A :|: C) :&: (B :|: C).
proof: Proof. by move=> A B C; apply/setP => x; rewrite !inE orb_andl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finset)