change with (\forall x:Z. x < x \to False).
intro.elim x.exact H.
cut (neg n < neg n \to False).
-apply Hcut.apply H.simplify.apply not_le_Sn_n.
+apply Hcut.apply H.simplify.unfold lt.apply not_le_Sn_n.
cut (pos n < pos n \to False).
-apply Hcut.apply H.simplify.apply not_le_Sn_n.
+apply Hcut.apply H.simplify.unfold lt.apply not_le_Sn_n.
qed.
theorem irrefl_Zlt: irreflexive Z Zlt