<commit_before>(*  Title:      ZF/ex/misc
    ID:         $Id$
    Author:     <NAME>, Cambridge University Computer Laboratory
    Copyright   1993  University of Cambridge

Miscellaneous examples for Zermelo-Fraenkel Set Theory 
Composition of homomorphisms, Pastre's examples, ...
*)

writeln"ZF/ex/misc";

(*Nice Blast_tac benchmark.  Proved in 0.3s; old tactics can't manage it!*)
goal ZF.thy "!!S. ALL x:S. ALL y:S. x<=y ==> EX z. S <= {z}";
by (Blast_tac 1);
result();

context Perm.thy;

(*Example 12 (credited to <NAME>) from
 <NAME>.  A Maximal Method for Set Variables in Automatic Theorem-proving.
 In: <NAME> and <NAME> and <NAME>, eds.  Machine Intelligence 9.<commit_msg>New example<commit_after>(*  Title:      ZF/ex/misc
    ID:         $Id$
    Author:     <NAME>, Cambridge University Computer Laboratory
    Copyright   1993  University of Cambridge

Miscellaneous examples for Zermelo-Fraenkel Set Theory 
Composition of homomorphisms, Pastre's examples, ...
*)

writeln"ZF/ex/misc";

(*Nice Blast_tac benchmark.  Proved in 0.3s; old tactics can't manage it!*)
goal ZF.thy "!!S. ALL x:S. ALL y:S. x<=y ==> EX z. S <= {z}";
by (Blast_tac 1);
result();

(*variant of the benchmark above*)
goal ZF.thy "!!S. ALL x:S. Union(S) <= x ==> EX z. S <= {z}";
by (Blast_tac 1);
result();

context Perm.thy;

(*Example 12 (credited to <NAME>) from
 <NAME>.  A Maximal Method for Set Variables in Automatic Theorem-proving.
 In: <NAME> and <NAME> and <NAME>, eds.  Machine Intelligence 9.
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