proposition: Lemma subU2_setP A B C : (sub (B\cup C) A) <-> (sub B A /\ sub C A).
proof: Proof. split. move => h;split; apply: (sub_trans _ h);[apply: subsetU2l |apply: subsetU2r]. by move => [h1 h2];apply: setU2_12S. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)