proposition: Lemma GE_prop2 E s : GT E s -> GL E s -> Law s E.
proof: Proof. move => ti [r1a r1b]; split. - by apply /setP_P. - by split => //; move => a /(GE_prop1 ti) []. - apply: extensionality => x. move/funI_P => [z zs ->]; move: (GE_prop1 ti zs) => [_ h2 h3 h4 _]. by rewrite -h2;apply: setXp_i. move/setX_P => [ha hb hc]. apply/funI_P; move: (r1a _ _ hb hc) => [c]; rewrite ha => zz. by exists (J x c) => //; aw. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)