--- 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