mod change (-x)

[helm.git] / helm / software / matita / contribs / ng_assembly / common / nat.ma

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 (executable)
new mode 100644 (file)
index 12ca65a..e84a76c
--- a/helm/software/matita/contribs/ng_assembly/common/nat.ma
+++ b/helm/software/matita/contribs/ng_assembly/common/nat.ma
@@ -16,7 +16,7 @@
 (*                          Progetto FreeScale                            *)
 (*                                                                        *)
 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
-(*   Ultima modifica: 05/08/2009                                          *)
+(*   Sviluppo: 2008-2010                                                  *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
@@ -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.