src/ZF/Nat.thy

+(*  Title: 	ZF/nat.thy
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+Natural numbers in Zermelo-Fraenkel Set Theory 
+*)
+
+Nat = Ord + Bool + 
+consts
+    nat 	::      "i"
+    nat_case    ::      "[i, i, i=>i]=>i"
+    nat_rec     ::      "[i, i, [i,i]=>i]=>i"
+
+rules
+
+    nat_def     "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
+
+    nat_case_def
+	"nat_case(k,a,b) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
+
+    nat_rec_def
+	"nat_rec(k,a,b) ==   \
+\   	  wfrec(Memrel(nat), k, %n f. nat_case(n, a, %m. b(m, f`m)))"
+
+end