proposition: Lemma setU2id_Pl A T: sub A T <-> A \cup T = T.
proof: Proof. split; last by move => <-;apply: subsetU2l. move => sat; apply: extensionality; last by apply: subsetU2r. by rewrite - {2}(setU2_id T); apply:setU2_S2. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)