proposition: Lemma setIP x A B : reflect (x \in A /\ x \in B) (x \in A :&: B).
proof: Proof. exact: (iffP (@setIdP _ _ _)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)