# HG changeset patch # User paulson # Date 859987722 -7200 # Node ID ac81a17f86f89b24bffd0f0bea2eabe3113443eb # Parent ba585d52ea4e7b55e618b1420704b33070327277 Moved definitions (binary intersection, etc.) from upair.thy back to ZF.thy diff -r ba585d52ea4e -r ac81a17f86f8 src/ZF/ZF.thy --- a/src/ZF/ZF.thy Wed Apr 02 15:26:52 1997 +0200 +++ b/src/ZF/ZF.thy Wed Apr 02 15:28:42 1997 +0200 @@ -196,7 +196,6 @@ and Powerset Axioms using the following definitions. *) Collect_def "Collect(A,P) == {y . x:A, x=y & P(x)}" - Inter_def "Inter(A) == { x:Union(A) . ALL y:A. x:y}" (*Unordered pairs (Upair) express binary union/intersection and cons; set enumerations translate as {a,...,z} = cons(a,...,cons(z,0)...)*) @@ -204,6 +203,17 @@ Upair_def "Upair(a,b) == {y. x:Pow(Pow(0)), (x=0 & y=a) | (x=Pow(0) & y=b)}" cons_def "cons(a,A) == Upair(a,a) Un A" + (* Difference, general intersection, binary union and small intersection *) + + Diff_def "A - B == { x:A . ~(x:B) }" + Inter_def "Inter(A) == { x:Union(A) . ALL y:A. x:y}" + Un_def "A Un B == Union(Upair(A,B))" + Int_def "A Int B == Inter(Upair(A,B))" + + (* Definite descriptions -- via Replace over the set "1" *) + + the_def "The(P) == Union({y . x:{0}, P(y)})" + if_def "if(P,a,b) == THE z. P & z=a | ~P & z=b" (* this "symmetric" definition works better than {{a}, {a,b}} *) Pair_def " == {{a,a}, {a,b}}" diff -r ba585d52ea4e -r ac81a17f86f8 src/ZF/upair.thy --- a/src/ZF/upair.thy Wed Apr 02 15:26:52 1997 +0200 +++ b/src/ZF/upair.thy Wed Apr 02 15:28:42 1997 +0200 @@ -3,19 +3,10 @@ Author: Lawrence C Paulson and Martin D Coen, CU Computer Laboratory Copyright 1993 University of Cambridge -Definitions involving unordered pairing +Dummy theory, but holds the standard ZF simpset. + (This is why the +end is present.) *) upair = ZF + -defs - (* Definite descriptions -- via Replace over the set "1" *) - the_def "The(P) == Union({y . x:{0}, P(y)})" - if_def "if(P,a,b) == THE z. P & z=a | ~P & z=b" - - (*Set difference; binary union and intersection*) - Diff_def "A - B == { x:A . ~(x:B) }" - Un_def "A Un B == Union(Upair(A,B))" - Int_def "A Int B == Inter(Upair(A,B))" - end