X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2FZ%2Fplus.ma;h=976f6cfb3ce01d379244fc66ec964a99563917d3;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=dc743e60bc77f384ecdadd927cee18d5ae085461;hpb=5a702cea95883f7095c16b450e065ccb1714fc5a;p=helm.git

diff --git a/helm/matita/library/Z/plus.ma b/helm/matita/library/Z/plus.ma
index dc743e60b..976f6cfb3 100644
--- a/helm/matita/library/Z/plus.ma
+++ b/helm/matita/library/Z/plus.ma
@@ -29,7 +29,7 @@ definition Zplus :Z \to Z \to Z \def
               match nat_compare m n with
                 [ LT \Rightarrow (neg (pred (n-m)))
                 | EQ \Rightarrow OZ
-                | GT \Rightarrow (pos (pred (m-n)))]]
+                | GT \Rightarrow (pos (pred (m-n)))] ]
     | (neg m) \Rightarrow
         match y with
          [ OZ \Rightarrow x
@@ -38,7 +38,7 @@ definition Zplus :Z \to Z \to Z \def
                 [ LT \Rightarrow (pos (pred (n-m)))
                 | EQ \Rightarrow OZ
                 | GT \Rightarrow (neg (pred (m-n)))]     
-         | (neg n) \Rightarrow (neg (pred ((S m)+(S n))))]].
+         | (neg n) \Rightarrow (neg (pred ((S m)+(S n))))] ].
 
 (*CSC: the URI must disappear: there is a bug now *)
 interpretation "integer plus" 'plus x y = (cic:/matita/Z/plus/Zplus.con x y).
@@ -59,12 +59,12 @@ simplify.
 rewrite < plus_n_Sm. rewrite < plus_n_Sm.rewrite < sym_plus.reflexivity.
 simplify.
 rewrite > nat_compare_n_m_m_n.
-simplify.elim nat_compare ? ?.simplify.reflexivity.
+simplify.elim nat_compare.simplify.reflexivity.
 simplify. reflexivity.
 simplify. reflexivity.
 elim y.simplify.reflexivity.
 simplify.rewrite > nat_compare_n_m_m_n.
-simplify.elim nat_compare ? ?.simplify.reflexivity.
+simplify.elim nat_compare.simplify.reflexivity.
 simplify. reflexivity.
 simplify. reflexivity.
 simplify.rewrite < plus_n_Sm. rewrite < plus_n_Sm.rewrite < sym_plus.reflexivity.
@@ -140,7 +140,7 @@ intros.elim x.
     apply Zplus_pos_pos.
     apply Zplus_pos_neg.
   elim y.
-    rewrite < sym_Zplus.rewrite < sym_Zplus (Zpred OZ).
+    rewrite < sym_Zplus.rewrite < (sym_Zplus (Zpred OZ)).
      rewrite < Zpred_Zplus_neg_O.rewrite > Zpred_Zsucc.simplify.reflexivity.
     apply Zplus_neg_pos.
     rewrite < Zplus_neg_neg.reflexivity.
@@ -154,8 +154,8 @@ qed.
 theorem Zplus_Zsucc_pos_neg: 
 \forall n,m. (Zsucc (pos n))+(neg m) = (Zsucc ((pos n)+(neg m))).
 intros.
-apply nat_elim2
-(\lambda n,m. (Zsucc (pos n))+(neg m) = (Zsucc ((pos n)+(neg m)))).intro.
+apply (nat_elim2
+(\lambda n,m. (Zsucc (pos n))+(neg m) = (Zsucc ((pos n)+(neg m))))).intro.
 intros.elim n1.
 simplify. reflexivity.
 elim n2.simplify. reflexivity.
@@ -169,10 +169,10 @@ elim H.reflexivity.
 qed.
 
 theorem Zplus_Zsucc_neg_neg : 
-\forall n,m. (Zsucc (neg n))+(neg m) = Zsucc ((neg n)+(neg m)).
+\forall n,m. Zsucc (neg n) + neg m = Zsucc (neg n + neg m).
 intros.
-apply nat_elim2
-(\lambda n,m. ((Zsucc (neg n))+(neg m)) = Zsucc ((neg n)+(neg m))).intro.
+apply (nat_elim2
+(\lambda n,m. Zsucc (neg n) + neg m = Zsucc (neg n + neg m))).intro.
 intros.elim n1.
 simplify. reflexivity.
 elim n2.simplify. reflexivity.
@@ -188,8 +188,8 @@ qed.
 theorem Zplus_Zsucc_neg_pos: 
 \forall n,m. Zsucc (neg n)+(pos m) = Zsucc ((neg n)+(pos m)).
 intros.
-apply nat_elim2
-(\lambda n,m. (Zsucc (neg n))+(pos m) = Zsucc ((neg n)+(pos m))).
+apply (nat_elim2
+(\lambda n,m. Zsucc (neg n) + (pos m) = Zsucc (neg n + pos m))).
 intros.elim n1.
 simplify. reflexivity.
 elim n2.simplify. reflexivity.
@@ -210,18 +210,18 @@ intros.elim x.
     simplify.reflexivity.
     rewrite < Zsucc_Zplus_pos_O.reflexivity.
   elim y.
-    rewrite < sym_Zplus OZ.reflexivity.
+    rewrite < (sym_Zplus OZ).reflexivity.
     apply Zplus_Zsucc_pos_pos.
     apply Zplus_Zsucc_pos_neg.
   elim y.
-    rewrite < sym_Zplus.rewrite < sym_Zplus OZ.simplify.reflexivity.
+    rewrite < sym_Zplus.rewrite < (sym_Zplus OZ).simplify.reflexivity.
     apply Zplus_Zsucc_neg_pos.
     apply Zplus_Zsucc_neg_neg.
 qed.
 
 theorem Zplus_Zpred: \forall x,y:Z. (Zpred x)+y = Zpred (x+y).
 intros.
-cut Zpred (x+y) = Zpred ((Zsucc (Zpred x))+y).
+cut (Zpred (x+y) = Zpred ((Zsucc (Zpred x))+y)).
 rewrite > Hcut.
 rewrite > Zplus_Zsucc.
 rewrite > Zpred_Zsucc.
@@ -232,20 +232,20 @@ qed.
 
 
 theorem associative_Zplus: associative Z Zplus.
-change with \forall x,y,z:Z. (x + y) + z = x + (y + z). 
+change with (\forall x,y,z:Z. (x + y) + z = x + (y + z)). 
 (* simplify. *)
 intros.elim x.
   simplify.reflexivity.
   elim n.
     rewrite < Zsucc_Zplus_pos_O.rewrite < Zsucc_Zplus_pos_O.
      rewrite > Zplus_Zsucc.reflexivity.
-    rewrite > Zplus_Zsucc (pos n1).rewrite > Zplus_Zsucc (pos n1).
-     rewrite > Zplus_Zsucc ((pos n1)+y).apply eq_f.assumption.
+    rewrite > (Zplus_Zsucc (pos n1)).rewrite > (Zplus_Zsucc (pos n1)).
+     rewrite > (Zplus_Zsucc ((pos n1)+y)).apply eq_f.assumption.
   elim n.
     rewrite < (Zpred_Zplus_neg_O (y+z)).rewrite < (Zpred_Zplus_neg_O y).
      rewrite < Zplus_Zpred.reflexivity.
-    rewrite > Zplus_Zpred (neg n1).rewrite > Zplus_Zpred (neg n1).
-     rewrite > Zplus_Zpred ((neg n1)+y).apply eq_f.assumption.
+    rewrite > (Zplus_Zpred (neg n1)).rewrite > (Zplus_Zpred (neg n1)).
+     rewrite > (Zplus_Zpred ((neg n1)+y)).apply eq_f.assumption.
 qed.
 
 variant assoc_Zplus : \forall x,y,z:Z.  (x+y)+z = x+(y+z)