--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/Cardinal.thy Tue Jun 21 17:20:34 1994 +0200
@@ -0,0 +1,33 @@
+(* Title: ZF/Cardinal.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1994 University of Cambridge
+
+Cardinals in Zermelo-Fraenkel Set Theory
+*)
+
+Cardinal = OrderType + Fixedpt + Nat + Sum +
+consts
+ Least :: "(i=>o) => i" (binder "LEAST " 10)
+ eqpoll, lepoll :: "[i,i] => o" (infixl 50)
+ "cardinal" :: "i=>i" ("|_|")
+ Card :: "i=>o"
+
+ swap :: "[i,i,i]=>i" (*not used; useful??*)
+
+rules
+
+ (*least ordinal operator*)
+ Least_def "Least(P) == THE i. Ord(i) & P(i) & (ALL j. j<i --> ~P(j))"
+
+ eqpoll_def "A eqpoll B == EX f. f: bij(A,B)"
+
+ lepoll_def "A lepoll B == EX f. f: inj(A,B)"
+
+ cardinal_def "|A| == LEAST i. i eqpoll A"
+
+ Card_def "Card(i) == ( i = |i| )"
+
+ swap_def "swap(A,x,y) == (lam z:A. if(z=x, y, if(z=y, x, z)))"
+
+end