definition total_order_property : ∀E:excess. Type ≝
λE:excess. ∀a,b:E. a ≰ b → b < a.
+
+lemma dual_exc: excess→ excess.
+intro E; apply mk_excess;
+[apply (exc_carr E);|apply (λx,y:E.y≰x);|apply exc_coreflexive;
+|unfold cotransitive; simplify;intros;cases (exc_cotransitive E ??z e);
+ [right|left]assumption]
+qed.