proposition: Lemma setI2id_Pl A T: sub A T <-> A \cap T = A.
proof: Proof. split; last by move => <-;apply: subsetI2r. move => sat; apply: extensionality; first by apply: subsetI2l. by rewrite - {1}(setI2_id A); apply:setI2_S1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)