
diff -r f04b33ce250f -r a4dc62a46ee4 Nat.thy
--- a/Nat.thy	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,70 +0,0 @@
-(*  Title:      HOL/Nat.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.
-*)
-
-Nat = WF +
-
-(** type ind **)
-
-types
-  ind
-
-arities
-  ind :: term
-
-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 *)
-
-subtype (Nat)
-  nat = "lfp(%X. {Zero_Rep} Un (Suc_Rep``X))"   (lfp_def)
-
-instance
-  nat :: ord
-
-
-(* abstract constants and syntax *)
-
-consts
-  "0"           :: "nat"                ("0")
-  Suc           :: "nat => nat"
-  nat_case      :: "['a, nat => 'a, nat] => 'a"
-  pred_nat      :: "(nat * nat) set"
-  nat_rec       :: "[nat, 'a, [nat, 'a] => 'a] => 'a"
-
-translations
-  "case p of 0 => a | Suc(y) => b" == "nat_case(a, %y.b, p)"
-
-defs
-  Zero_def      "0 == Abs_Nat(Zero_Rep)"
-  Suc_def       "Suc == (%n. Abs_Nat(Suc_Rep(Rep_Nat(n))))"
-
-  (*nat operations and recursion*)
-  nat_case_def  "nat_case(a, f, n) == @z.  (n=0 --> z=a)  
-                                        & (!x. n=Suc(x) --> z=f(x))"
-  pred_nat_def  "pred_nat == {p. ? n. p = <n, Suc(n)>}"
-
-  less_def "m<n == <m,n>:trancl(pred_nat)"
-
-  le_def   "m<=(n::nat) == ~(n<m)"
-
-  nat_rec_def   "nat_rec(n, c, d) == wfrec(pred_nat, n,   
-                        nat_case(%g.c, %m g. d(m, g(m))))"
-end




