diff -r 4d1614d8f119 -r 70b789956bd3 src/ZF/CardinalArith.thy --- a/src/ZF/CardinalArith.thy Thu Jul 21 16:51:26 1994 +0200 +++ b/src/ZF/CardinalArith.thy Tue Jul 26 13:21:20 1994 +0200 @@ -6,22 +6,18 @@ Cardinal Arithmetic *) -CardinalArith = Cardinal + OrderArith + Arith + +CardinalArith = Cardinal + OrderArith + Arith + Fin + consts - jump_cardinal :: "i=>i" InfCard :: "i=>o" "|*|" :: "[i,i]=>i" (infixl 70) "|+|" :: "[i,i]=>i" (infixl 65) csquare_rel :: "i=>i" + jump_cardinal :: "i=>i" + csucc :: "i=>i" rules - jump_cardinal_def - "jump_cardinal(K) == \ -\ UN X:Pow(K). {z. r: Pow(X*X), well_ord(X,r) & z = ordertype(X,r)}" - - InfCard_def "InfCard(i) == Card(i) & nat le i" cadd_def "i |+| j == | i+j |" @@ -33,4 +29,13 @@ \ rmult(k,Memrel(k), k*k, \ \ rmult(k,Memrel(k), k,Memrel(k))))" + (*This def is more complex than Kunen's but it more easily proved to + be a cardinal*) + jump_cardinal_def + "jump_cardinal(K) == \ +\ UN X:Pow(K). {z. r: Pow(K*K), well_ord(X,r) & z = ordertype(X,r)}" + + (*needed because jump_cardinal(K) might not be the successor of K*) + csucc_def "csucc(K) == LEAST L. Card(L) & K