proposition: Lemma Exercise2_8a r: order r -> anti_directed r -> ramified r.
proof: Proof. move=> or /(Exercise1_23hP or) [p1 p2]. move=> x y xy; move: (p1 _ _ xy) => [z xz p3]; exists z. have zz: (gle r z z) by order_tac; order_tac. have yy: (gle r y y) by order_tac; order_tac. split => //;[ move=> yz; exact (p3 _ yz zz)| move=> zy;exact: (p3 _ yy zy)]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)