-apply nat_elim2 (\lambda n,m.\lnot (n \leq m) \to m<n).
-intros.apply absurd (O \leq n1).apply le_O_n.assumption.
-simplify.intros.apply le_S_S.apply le_O_n.
-simplify.intros.apply le_S_S.apply H.intros.apply H1.apply le_S_S.
+apply (nat_elim2 (\lambda n,m.n \nleq m \to m<n)).
+intros.apply (absurd (O \leq n1)).apply le_O_n.assumption.
+unfold Not.unfold lt.intros.apply le_S_S.apply le_O_n.
+unfold Not.unfold lt.intros.apply le_S_S.apply H.intros.apply H1.apply le_S_S.