--- 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