proposition: Lemma GE_prop1 E s a: GT E s -> inc a s -> [/\ pairp a, pairp (P a), inc (P (P a)) E, inc (Q (P a)) E & inc (Q a) E].
proof: Proof. move /setP_P => ha hb. by move: (ha _ hb) => /setX_P [ra /setX_P[rb rc rd] re]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)