proposition: Lemma Exercise1_11i r: complete_lattice r -> complete_lattice (opp_order r).
proof: Proof. move => [p1 p2]. move: (opp_osr p1) => [q3 q4];split => //;rewrite q4. move=> X Xs; move: (p2 _ Xs) => [[x p3] [y p4]]; split. by exists y; apply/inf_sup_oppP. by exists x; apply/sup_inf_oppP. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)