X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2FZ.ma;h=ba10847201dee7b650afc34e8febb2353731bfe4;hb=5d5e328a05ed70fcf565aef8f92b7ec87b2740f2;hp=da6bbadb28bd5c9a0edd9d54f7df0419f7af7bbb;hpb=49734f6f824dd310520cbb0cee0e605296e2d975;p=helm.git

diff --git a/helm/matita/library/Z.ma b/helm/matita/library/Z.ma
index da6bbadb2..ba1084720 100644
--- a/helm/matita/library/Z.ma
+++ b/helm/matita/library/Z.ma
@@ -126,21 +126,21 @@ simplify.reflexivity.
 qed.
 
 theorem sym_Zplus : \forall x,y:Z. eq Z (Zplus x y) (Zplus y x).
-intros.elim x.simplify.rewrite > Zplus_z_O y.reflexivity.
+intros.elim x.simplify.rewrite > Zplus_z_O.reflexivity.
 elim y.simplify.reflexivity.
 simplify.
-rewrite < (sym_plus e e1).reflexivity.
+rewrite < sym_plus.reflexivity.
 simplify.
-rewrite > nat_compare_invert e1 e2.
-simplify.elim nat_compare e2 e1.simplify.reflexivity.
+rewrite > nat_compare_invert.
+simplify.elim nat_compare ? ?.simplify.reflexivity.
 simplify. reflexivity.
 simplify. reflexivity.
 elim y.simplify.reflexivity.
-simplify.rewrite > nat_compare_invert e1 e2.
-simplify.elim nat_compare e2 e1.simplify.reflexivity.
+simplify.rewrite > nat_compare_invert.
+simplify.elim nat_compare ? ?.simplify.reflexivity.
 simplify. reflexivity.
 simplify. reflexivity.
-simplify.elim (sym_plus e2 e).reflexivity.
+simplify.elim (sym_plus ? ?).reflexivity.
 qed.
 
 theorem Zpred_neg : \forall z:Z. eq Z (Zpred z) (Zplus (neg O) z).
@@ -167,9 +167,9 @@ simplify.reflexivity.
 simplify.reflexivity.
 elim m.
 simplify.
-rewrite < plus_n_O e1.reflexivity.
+rewrite < plus_n_O.reflexivity.
 simplify.
-rewrite < plus_n_Sm e1 e.reflexivity.
+rewrite < plus_n_Sm.reflexivity.
 qed.
 
 theorem Zplus_succ_pred_pn :
@@ -195,23 +195,21 @@ elim n.elim m.
 simplify.reflexivity.
 simplify.reflexivity.
 elim m.
-simplify.rewrite < plus_n_Sm e1 O.reflexivity.
-simplify.rewrite > plus_n_Sm e1 (S e).reflexivity.
+simplify.rewrite < plus_n_Sm.reflexivity.
+simplify.rewrite > plus_n_Sm.reflexivity.
 qed.
 
-(* da qui in avanti rewrite ancora non utilizzata *)
-
 theorem Zplus_succ_pred:
 \forall x,y. eq Z (Zplus x y) (Zplus (Zsucc x) (Zpred y)).
 intros.
 elim x. elim y.
 simplify.reflexivity.
 simplify.reflexivity.
-elim (Zsucc_pos ?).elim (sym_eq ? ? ? (Zsucc_pred ?)).reflexivity.
-elim y.elim sym_Zplus ? ?.elim sym_Zplus (Zpred OZ) ?.
-elim (Zpred_neg ?).elim (sym_eq ? ? ? (Zpred_succ ?)).
+rewrite < Zsucc_pos.rewrite > Zsucc_pred.reflexivity.
+elim y.rewrite < sym_Zplus.rewrite < sym_Zplus (Zpred OZ).
+rewrite < Zpred_neg.rewrite > Zpred_succ.
 simplify.reflexivity.
-apply Zplus_succ_pred_nn.
+rewrite < Zplus_succ_pred_nn.reflexivity.
 apply Zplus_succ_pred_np.
 elim y.simplify.reflexivity.
 apply Zplus_succ_pred_pn.
@@ -236,7 +234,7 @@ intros. elim n1.
 simplify. reflexivity.
 simplify.reflexivity.
 intros.
-elim (Zplus_succ_pred_pn ? m1).
+rewrite < (Zplus_succ_pred_pn ? m1).
 elim H.reflexivity.
 qed.
 
@@ -253,7 +251,7 @@ intros. elim n1.
 simplify. reflexivity.
 simplify.reflexivity.
 intros.
-elim (Zplus_succ_pred_nn ? m1).
+rewrite < (Zplus_succ_pred_nn ? m1).
 reflexivity.
 qed.
 
@@ -270,8 +268,8 @@ intros. elim n1.
 simplify. reflexivity.
 simplify.reflexivity.
 intros.
-elim H.
-elim (Zplus_succ_pred_np ? (S m1)).
+rewrite < H.
+rewrite < (Zplus_succ_pred_np ? (S m1)).
 reflexivity.
 qed.
 
@@ -279,13 +277,13 @@ qed.
 theorem Zsucc_plus : \forall x,y:Z. eq Z (Zplus (Zsucc x) y) (Zsucc (Zplus x y)).
 intros.elim x.elim y.
 simplify. reflexivity.
-elim (Zsucc_pos ?).reflexivity.
+rewrite < Zsucc_pos.reflexivity.
 simplify.reflexivity.
-elim y.elim sym_Zplus ? ?.elim sym_Zplus OZ ?.simplify.reflexivity.
+elim y.rewrite < sym_Zplus.rewrite < sym_Zplus OZ.simplify.reflexivity.
 apply Zsucc_plus_nn.
 apply Zsucc_plus_np.
 elim y.
-elim (sym_Zplus OZ ?).reflexivity.
+rewrite < sym_Zplus OZ.reflexivity.
 apply Zsucc_plus_pn.
 apply Zsucc_plus_pp.
 qed.
@@ -293,30 +291,31 @@ qed.
 theorem Zpred_plus : \forall x,y:Z. eq Z (Zplus (Zpred x) y) (Zpred (Zplus x y)).
 intros.
 cut eq Z (Zpred (Zplus x y)) (Zpred (Zplus (Zsucc (Zpred x)) y)).
-elim (sym_eq ? ? ? Hcut).
-elim (sym_eq ? ? ? (Zsucc_plus ? ?)).
-elim (sym_eq ? ? ? (Zpred_succ ?)).
+rewrite > Hcut.
+rewrite > Zsucc_plus.
+rewrite > Zpred_succ.
 reflexivity.
-elim (sym_eq ? ? ? (Zsucc_pred ?)).
+rewrite > Zsucc_pred.
 reflexivity.
 qed.
 
 theorem assoc_Zplus : 
 \forall x,y,z:Z. eq Z (Zplus x (Zplus y z)) (Zplus (Zplus x y) z).
 intros.elim x.simplify.reflexivity.
-elim e1.elim (Zpred_neg (Zplus y z)).
-elim (Zpred_neg y).
-elim (Zpred_plus ? ?).
+elim e1.rewrite < (Zpred_neg (Zplus y z)).
+rewrite < (Zpred_neg y).
+rewrite < Zpred_plus.
 reflexivity.
-elim (sym_eq ? ? ? (Zpred_plus (neg e) ?)).
-elim (sym_eq ? ? ? (Zpred_plus (neg e) ?)).
-elim (sym_eq ? ? ? (Zpred_plus (Zplus (neg e) y) ?)).
+rewrite > Zpred_plus (neg e).
+rewrite > Zpred_plus (neg e).
+rewrite > Zpred_plus (Zplus (neg e) y).
 apply f_equal.assumption.
-elim e2.elim (Zsucc_pos ?).
-elim (Zsucc_pos ?).
-apply (sym_eq ? ? ? (Zsucc_plus ? ?)) .
-elim (sym_eq ? ? ? (Zsucc_plus (pos e1) ?)).
-elim (sym_eq ? ? ? (Zsucc_plus (pos e1) ?)).
-elim (sym_eq ? ? ? (Zsucc_plus (Zplus (pos e1) y) ?)).
+elim e2.rewrite < Zsucc_pos.
+rewrite < Zsucc_pos.
+rewrite > Zsucc_plus.
+reflexivity.
+rewrite > Zsucc_plus (pos e1).
+rewrite > Zsucc_plus (pos e1).
+rewrite > Zsucc_plus (Zplus (pos e1) y).
 apply f_equal.assumption.
 qed.