fixed according to the new fresh name generator

diff --git a/helm/matita/library/Z.ma b/helm/matita/library/Z.ma
index d0049187a6a2510ef6b463156689491455ccdf50..da6bbadb28bd5c9a0edd9d54f7df0419f7af7bbb 100644 (file)
--- a/helm/matita/library/Z.ma
+++ b/helm/matita/library/Z.ma
@@ -51,13 +51,13 @@ theorem OZ_discr :
 \forall z. if_then_else (OZ_testb z) (eq Z z OZ) (Not (eq Z z OZ)). 
 intros.elim z.simplify.reflexivity.
 simplify.intros.
-cut match neg e with 
+cut match neg e1 with 
 [ OZ \Rightarrow True 
 | (pos n) \Rightarrow False
 | (neg n) \Rightarrow False].
 apply Hcut.rewrite > H.simplify.exact I.
 simplify.intros.
-cut match pos e with 
+cut match pos e2 with 
 [ OZ \Rightarrow True 
 | (pos n) \Rightarrow False
 | (neg n) \Rightarrow False].
@@ -84,7 +84,7 @@ definition Zpred \def
 
 theorem Zpred_succ: \forall z:Z. eq Z (Zpred (Zsucc z)) z.
 intros.elim z.reflexivity.
-elim e.reflexivity.
+elim e1.reflexivity.
 reflexivity.
 reflexivity.
 qed.
@@ -92,7 +92,7 @@ qed.
 theorem Zsucc_pred: \forall z:Z. eq Z (Zsucc (Zpred z)) z.
 intros.elim z.reflexivity.
 reflexivity.
-elim e.reflexivity.
+elim e2.reflexivity.
 reflexivity.
 qed.
 
@@ -131,30 +131,30 @@ elim y.simplify.reflexivity.
 simplify.
 rewrite < (sym_plus e e1).reflexivity.
 simplify.
-rewrite > nat_compare_invert e e1.
-simplify.elim nat_compare e1 e.simplify.reflexivity.
+rewrite > nat_compare_invert e1 e2.
+simplify.elim nat_compare e2 e1.simplify.reflexivity.
 simplify. reflexivity.
 simplify. reflexivity.
 elim y.simplify.reflexivity.
-simplify.rewrite > nat_compare_invert e e1.
-simplify.elim nat_compare e1 e.simplify.reflexivity.
+simplify.rewrite > nat_compare_invert e1 e2.
+simplify.elim nat_compare e2 e1.simplify.reflexivity.
 simplify. reflexivity.
 simplify. reflexivity.
-simplify.elim (sym_plus e1 e).reflexivity.
+simplify.elim (sym_plus e2 e).reflexivity.
 qed.
 
 theorem Zpred_neg : \forall z:Z. eq Z (Zpred z) (Zplus (neg O) z).
 intros.elim z.
 simplify.reflexivity.
 simplify.reflexivity.
-elim e.simplify.reflexivity.
+elim e2.simplify.reflexivity.
 simplify.reflexivity.
 qed.
 
 theorem Zsucc_pos : \forall z:Z. eq Z (Zsucc z) (Zplus (pos O) z).
 intros.elim z.
 simplify.reflexivity.
-elim e.simplify.reflexivity.
+elim e1.simplify.reflexivity.
 simplify.reflexivity.
 simplify.reflexivity.
 qed.
@@ -167,9 +167,9 @@ simplify.reflexivity.
 simplify.reflexivity.
 elim m.
 simplify.
-rewrite < plus_n_O e.reflexivity.
+rewrite < plus_n_O e1.reflexivity.
 simplify.
-rewrite < plus_n_Sm e e1.reflexivity.
+rewrite < plus_n_Sm e1 e.reflexivity.
 qed.
 
 theorem Zplus_succ_pred_pn :
@@ -195,11 +195,12 @@ elim n.elim m.
 simplify.reflexivity.
 simplify.reflexivity.
 elim m.
-simplify.rewrite < plus_n_Sm e O.reflexivity.
-simplify.rewrite > plus_n_Sm e (S e1).reflexivity.
+simplify.rewrite < plus_n_Sm e1 O.reflexivity.
+simplify.rewrite > plus_n_Sm e1 (S e).reflexivity.
 qed.
 
-(*CSC: da qui in avanti rewrite ancora non utilizzata *)
+(* 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.
@@ -229,7 +230,7 @@ apply nat_double_ind
 (\lambda n,m. eq Z (Zplus (Zsucc (pos n)) (neg m)) (Zsucc (Zplus (pos n) (neg m)))).intro.
 intros.elim n1.
 simplify. reflexivity.
-elim e.simplify. reflexivity.
+elim e1.simplify. reflexivity.
 simplify. reflexivity.
 intros. elim n1.
 simplify. reflexivity.
@@ -246,7 +247,7 @@ apply nat_double_ind
 (\lambda n,m. eq Z (Zplus (Zsucc (neg n)) (neg m)) (Zsucc (Zplus (neg n) (neg m)))).intro.
 intros.elim n1.
 simplify. reflexivity.
-elim e.simplify. reflexivity.
+elim e1.simplify. reflexivity.
 simplify. reflexivity.
 intros. elim n1.
 simplify. reflexivity.
@@ -263,7 +264,7 @@ apply nat_double_ind
 (\lambda n,m. eq Z (Zplus (Zsucc (neg n)) (pos m)) (Zsucc (Zplus (neg n) (pos m)))).
 intros.elim n1.
 simplify. reflexivity.
-elim e.simplify. reflexivity.
+elim e1.simplify. reflexivity.
 simplify. reflexivity.
 intros. elim n1.
 simplify. reflexivity.
@@ -303,15 +304,15 @@ 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 e.elim (Zpred_neg (Zplus y z)).
+elim e1.elim (Zpred_neg (Zplus y z)).
 elim (Zpred_neg y).
 elim (Zpred_plus ? ?).
 reflexivity.
-elim (sym_eq ? ? ? (Zpred_plus (neg e1) ?)).
-elim (sym_eq ? ? ? (Zpred_plus (neg e1) ?)).
-elim (sym_eq ? ? ? (Zpred_plus (Zplus (neg e1) y) ?)).
+elim (sym_eq ? ? ? (Zpred_plus (neg e) ?)).
+elim (sym_eq ? ? ? (Zpred_plus (neg e) ?)).
+elim (sym_eq ? ? ? (Zpred_plus (Zplus (neg e) y) ?)).
 apply f_equal.assumption.
-elim e.elim (Zsucc_pos ?).
+elim e2.elim (Zsucc_pos ?).
 elim (Zsucc_pos ?).
 apply (sym_eq ? ? ? (Zsucc_plus ? ?)) .
 elim (sym_eq ? ? ? (Zsucc_plus (pos e1) ?)).

diff --git a/helm/matita/library/nat.ma b/helm/matita/library/nat.ma
index 3ab39d9e485883e51868263d0b47c64cb42aebff..4ab1feb2b84873e1898cc9e1c3ed68de98b9fe1e 100644 (file)
--- a/helm/matita/library/nat.ma
+++ b/helm/matita/library/nat.ma
@@ -103,8 +103,8 @@ theorem times_n_Sm :
 \forall n,m:nat. eq nat (plus n (times n  m)) (times n (S m)).
 intros.elim n.simplify.reflexivity.
 simplify.apply f_equal.rewrite < H.
-transitivity (plus (plus e m) (times e m)).symmetry.
-apply assoc_plus.transitivity (plus (plus m e) (times e m)).
+transitivity (plus (plus e1 m) (times e1 m)).symmetry.
+apply assoc_plus.transitivity (plus (plus m e1) (times e1 m)).
 apply f_equal2.
 apply sym_plus.reflexivity.apply assoc_plus.
 qed.
@@ -188,7 +188,7 @@ qed.
 
 theorem le_Sn_n : \forall n:nat. Not (le (S n) n).
 intros.elim n.apply le_Sn_O.simplify.intros.
-cut le (S e) e.apply H.assumption.apply le_S_n.assumption.
+cut le (S e1) e1.apply H.assumption.apply le_S_n.assumption.
 qed.
 
 theorem le_antisym : \forall n,m:nat. (le n m) \to (le m n) \to (eq nat n m).