ocaml 3.09 transition

[helm.git] / helm / matita / library / nat / exp.ma

diff --git a/helm/matita/library/nat/exp.ma b/helm/matita/library/nat/exp.ma
index 19c09e27ccb6ae27633fa7809ced27cd71c73cbc..11d84f74ca7deb3b676007693f72b585c0547435 100644 (file)
--- a/helm/matita/library/nat/exp.ma
+++ b/helm/matita/library/nat/exp.ma
@@ -48,15 +48,15 @@ rewrite < times_n_Sm.reflexivity.
 qed.
 
 theorem lt_O_exp: \forall n,m:nat. O < n \to O < n \sup m. 
-intros.elim m.simplify.apply le_n.
-simplify.rewrite > times_n_SO.
+intros.elim m.simplify.unfold lt.apply le_n.
+simplify.unfold lt.rewrite > times_n_SO.
 apply le_times.assumption.assumption.
 qed.
 
 theorem lt_m_exp_nm: \forall n,m:nat. (S O) < n \to m < n \sup m.
-intros.elim m.simplify.reflexivity.
-simplify.
-apply trans_le ? ((S(S O))*(S n1)).
+intros.elim m.simplify.unfold lt.reflexivity.
+simplify.unfold lt.
+apply (trans_le ? ((S(S O))*(S n1))).
 simplify.
 rewrite < plus_n_Sm.apply le_S_S.apply le_S_S.
 rewrite < sym_plus.
@@ -67,7 +67,7 @@ qed.
 theorem exp_to_eq_O: \forall n,m:nat. (S O) < n 
 \to n \sup m = (S O) \to m = O.
 intros.apply antisym_le.apply le_S_S_to_le.
-rewrite < H1.change with m < n \sup m.
+rewrite < H1.change with (m < n \sup m).
 apply lt_m_exp_nm.assumption.
 apply le_O_n.
 qed.
@@ -75,21 +75,21 @@ qed.
 theorem injective_exp_r: \forall n:nat. (S O) < n \to 
 injective nat nat (\lambda m:nat. n \sup m).
 simplify.intros 4.
-apply nat_elim2 (\lambda x,y.n \sup x = n \sup y \to x = y).
-intros.apply sym_eq.apply exp_to_eq_O n.assumption.
+apply (nat_elim2 (\lambda x,y.n \sup x = n \sup y \to x = y)).
+intros.apply sym_eq.apply (exp_to_eq_O n).assumption.
 rewrite < H1.reflexivity.
-intros.apply exp_to_eq_O n.assumption.assumption.
+intros.apply (exp_to_eq_O n).assumption.assumption.
 intros.apply eq_f.
 apply H1.
 (* esprimere inj_times senza S *)
-cut \forall a,b:nat.O < n \to n*a=n*b \to a=b.
-apply Hcut.simplify. apply le_S_S_to_le. apply le_S. assumption.
+cut (\forall a,b:nat.O < n \to n*a=n*b \to a=b).
+apply Hcut.simplify.unfold lt.apply le_S_S_to_le. apply le_S. assumption.
 assumption.
 intros 2.
-apply nat_case n.
-intros.apply False_ind.apply not_le_Sn_O O H3.
+apply (nat_case n).
+intros.apply False_ind.apply (not_le_Sn_O O H3).
 intros.
-apply inj_times_r m1.assumption.
+apply (inj_times_r m1).assumption.
 qed.
 
 variant inj_exp_r: \forall p:nat. (S O) < p \to \forall n,m:nat.