(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/RELATIONAL/NLE/order".
+
include "NLE/inv.ma".
\forall z. y <= z \to x <= z.
intros 3. elim H; clear H x y;
[ autobatch
- | lapply linear nle_inv_succ_1 to H3. decompose. subst.
+ | lapply linear nle_inv_succ_1 to H3. decompose. destruct.
autobatch
].
qed.
qed.
theorem nle_irrefl_ei: \forall x, z. z <= x \to z = succ x \to False.
- intros 3. elim H; clear H x z; subst. autobatch.
+ intros 3. elim H; clear H x z; destruct. autobatch.
qed.
theorem nle_irrefl_smart: \forall x. x < x \to False.