enable static binding of C/OCaml glue code

[helm.git] / helm / matita / library / Z.ma

diff --git a/helm/matita/library/Z.ma b/helm/matita/library/Z.ma
index 842b952b902ce2b57bf2f901e6331c6bc80a6aed..da6bbadb28bd5c9a0edd9d54f7df0419f7af7bbb 100644 (file)
--- a/helm/matita/library/Z.ma
+++ b/helm/matita/library/Z.ma
@@ -14,30 +14,7 @@
 
 set "baseuri" "cic:/matita/Z/".
 
-alias id "nat" = "cic:/matita/nat/nat.ind#xpointer(1/1)".
-alias id "O" = "cic:/matita/nat/nat.ind#xpointer(1/1/1)".
-alias id "false" = "cic:/matita/bool/bool.ind#xpointer(1/1/2)".
-alias id "true" = "cic:/matita/bool/bool.ind#xpointer(1/1/1)".
-alias id "Not" = "cic:/matita/logic/Not.con".
-alias id "eq" = "cic:/matita/equality/eq.ind#xpointer(1/1)".
-alias id "if_then_else" = "cic:/matita/bool/if_then_else.con".
-alias id "refl_equal" = "cic:/matita/equality/eq.ind#xpointer(1/1/1)".
-alias id "False" = "cic:/matita/logic/False.ind#xpointer(1/1)".
-alias id "True" = "cic:/matita/logic/True.ind#xpointer(1/1)".
-alias id "sym_eq" = "cic:/matita/equality/sym_eq.con".
-alias id "I" = "cic:/matita/logic/True.ind#xpointer(1/1/1)".
-alias id "S" = "cic:/matita/nat/nat.ind#xpointer(1/1/2)".
-alias id "LT" = "cic:/matita/compare/compare.ind#xpointer(1/1/1)".
-alias id "minus" = "cic:/matita/nat/minus.con".
-alias id "nat_compare" = "cic:/matita/nat/nat_compare.con".
-alias id "plus" = "cic:/matita/nat/plus.con".
-alias id "pred" = "cic:/matita/nat/pred.con".
-alias id "sym_plus" = "cic:/matita/nat/sym_plus.con".
-alias id "nat_compare_invert" = "cic:/matita/nat/nat_compare_invert.con".
-alias id "plus_n_O" = "cic:/matita/nat/plus_n_O.con".
-alias id "plus_n_Sm" = "cic:/matita/nat/plus_n_Sm.con".
-alias id "nat_double_ind" = "cic:/matita/nat/nat_double_ind.con".
-alias id "f_equal" = "cic:/matita/equality/f_equal.con".
+include "nat.ma".
 
 inductive Z : Set \def
   OZ : Z
@@ -74,13 +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].
@@ -107,7 +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.
@@ -115,7 +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.
 
@@ -154,30 +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.
@@ -190,9 +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 :
@@ -218,11 +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.
@@ -252,7 +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.
@@ -269,7 +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.
@@ -286,7 +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.
@@ -326,15 +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) ?)).