X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_assembly%2Fcommon%2Fnat.ma;h=e84a76c902fa1aec41f3f64f39f54b19f280ea59;hb=HEAD;hp=fe976cba632dee64756f67256047eae4b9f080f7;hpb=0f13d14b63b012e0ea8ce0d0e71bf808fdd444eb;p=helm.git

diff --git a/helm/software/matita/contribs/ng_assembly/common/nat.ma b/helm/software/matita/contribs/ng_assembly/common/nat.ma
old mode 100755
new mode 100644
index fe976cba6..e84a76c90
--- a/helm/software/matita/contribs/ng_assembly/common/nat.ma
+++ b/helm/software/matita/contribs/ng_assembly/common/nat.ma
@@ -38,6 +38,12 @@ default "natural numbers" cic:/matita/common/nat/nat.ind.
 alias num (instance 0) = "natural number".
 *)
 
+nlet rec nat_it (T:Type) (f:T → T) (arg:T) (n:nat) on n ≝
+ match n with
+  [ O ⇒ arg
+  | S n' ⇒ nat_it T f (f arg) n'
+  ].
+
 ndefinition nat1 ≝ S O.
 ndefinition nat2 ≝ S nat1.
 ndefinition nat3 ≝ S nat2.
@@ -207,13 +213,13 @@ interpretation "natural divide" 'divide x y = (div x y).
 
 ndefinition pred ≝ λn.match n with [ O ⇒ O | S n ⇒ n ].
 
-ndefinition nat128 ≝ nat64 * nat2.
-ndefinition nat256 ≝ nat128 * nat2.
-ndefinition nat512 ≝ nat256 * nat2.
-ndefinition nat1024 ≝ nat512 * nat2.
-ndefinition nat2048 ≝ nat1024 * nat2.
-ndefinition nat4096 ≝ nat2048 * nat2.
-ndefinition nat8192 ≝ nat4096 * nat2.
-ndefinition nat16384 ≝ nat8192 * nat2.
-ndefinition nat32768 ≝ nat16384 * nat2.
-ndefinition nat65536 ≝ nat32768 * nat2.
+ndefinition nat128 ≝ nat64 + nat64.
+ndefinition nat256 ≝ nat128 + nat128.
+ndefinition nat512 ≝ nat256 + nat256.
+ndefinition nat1024 ≝ nat512 + nat512.
+ndefinition nat2048 ≝ nat1024 + nat1024.
+ndefinition nat4096 ≝ nat2048 + nat2048.
+ndefinition nat8192 ≝ nat4096 + nat4096.
+ndefinition nat16384 ≝ nat8192 + nat8192.
+ndefinition nat32768 ≝ nat16384 + nat16384.
+ndefinition nat65536 ≝ nat32768 + nat32768.