proposition: Lemma setUP x A B : reflect (x \in A \/ x \in B) (x \in A :|: B).
proof: Proof. by rewrite !inE; apply: orP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)