proposition: Lemma total_order_lt_or_ge : forall (To:total_order R) x y, lt x y \/ ge x y.
proof: Proof. Proof using. intros. branches (total_order_lt_or_eq_or_gt To x y). left~. right~. subst. hnf. apply~ total_order_refl. right~. rewrite~ total_order_ge_is_rclosure_gt. total_order_normalize. hnfs~. Qed.
imports: TLC(LibTactics LibLogic LibReflect LibOperation LibRelation)