
diff -r 3470596f3cd5 -r 3196f93030bb src/HOL/NatDef.thy
--- a/src/HOL/NatDef.thy	Mon Aug 05 12:00:51 2002 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,70 +0,0 @@
-(*  Title:      HOL/NatDef.thy
-    ID:         $Id$
-    Author:     Tobias Nipkow, Cambridge University Computer Laboratory
-    Copyright   1991  University of Cambridge
-
-Definition of types ind and nat.
-
-Type nat is defined as a set Nat over type ind.
-*)
-
-NatDef = Wellfounded_Recursion +
-
-(** type ind **)
-
-types ind
-arities ind :: type
-
-consts
-  Zero_Rep      :: ind
-  Suc_Rep       :: ind => ind
-
-rules
-  (*the axiom of infinity in 2 parts*)
-  inj_Suc_Rep           "inj(Suc_Rep)"
-  Suc_Rep_not_Zero_Rep  "Suc_Rep(x) ~= Zero_Rep"
-
-
-
-(** type nat **)
-
-(* type definition *)
-
-consts
-  Nat' :: "ind set"
-
-inductive Nat'
-intrs
-  Zero_RepI "Zero_Rep : Nat'"
-  Suc_RepI  "i : Nat' ==> Suc_Rep i : Nat'"
-
-global
-
-typedef (Nat)
-  nat = "Nat'"   (Nat'.Zero_RepI)
-
-instance
-  nat :: {ord, zero, one}
-
-
-(* abstract constants and syntax *)
-
-consts
-  Suc       :: nat => nat
-  pred_nat  :: "(nat * nat) set"
-
-local
-
-defs
-  Zero_nat_def  "0 == Abs_Nat(Zero_Rep)"
-  Suc_def       "Suc == (%n. Abs_Nat(Suc_Rep(Rep_Nat(n))))"
-  One_nat_def	"1 == Suc 0"
-
-  (*nat operations*)
-  pred_nat_def  "pred_nat == {(m,n). n = Suc m}"
-
-  less_def      "m<n == (m,n):trancl(pred_nat)"
-
-  le_def        "m<=(n::nat) == ~(n<m)"
-
-end




