Return-Path: Delivery-Date: Received: from ted.cs.uidaho.edu (no rfc931) by swan.cl.cam.ac.uk with SMTP (PP-6.4) outside ac.uk; Tue, 2 Mar 1993 11:31:02 +0000 Received: by ted.cs.uidaho.edu (16.6/1.34) id AA06225; Tue, 2 Mar 93 03:19:26 -0800 Sender: info-hol-request@edu.uidaho.cs.ted Errors-To: info-hol-request@edu.uidaho.cs.ted Precedence: bulk Received: from swan.cl.cam.ac.uk by ted.cs.uidaho.edu (16.6/1.34) id AA06220; Tue, 2 Mar 93 03:19:16 -0800 Received: from razorbill.cl.cam.ac.uk (user jg (rfc931)) by swan.cl.cam.ac.uk with SMTP (PP-6.4) to cl; Tue, 2 Mar 1993 11:18:40 +0000 To: info-hol@edu.uidaho.cs.ted Cc: blok@nl.utwente.cs (Rintcius Blok) Subject: Re: pair proof In-Reply-To: Your message of Tue, 02 Mar 93 11:14:23 +0100. <9303021014.AA00306@apollo.cs.utwente.nl> Date: Tue, 02 Mar 93 11:18:25 +0000 From: Jim Grundy Message-Id: <"swan.cl.ca.782:02.03.93.11.18.47"@cl.cam.ac.uk> ... > I have a problem with proving the following goal: > > g "!P.(!(x:*) (y:**).x IN X /\ y IN Y==>P(x,y))= > (!z.(FST z) IN X /\ (SND z) IN Y ==>P z)";; > > I think the proof is not difficult and can be very short, > but I cannot find/derive an appropriate theorem to "jump" from > the first pair repr. to the second. ... > thanks, > Rintcius Blok. Hi, I would recomend using the pair library released with the latest version of HOL (but then I'm sort of likely to). There was, sadly, a bug with the version released with HOL2.01, but it should still work for this case, and at any rate the fix may be ftp'd from ftp.cl.cam.ac.uk: hvg/contrib/bugfixes/pair_lib Anyway... with the pair library loaded, the proof is simply: (GEN_TAC THEN (CONV_TAC (RATOR_CONV (RAND_CONV UNCURRY_FORALL_CONV))) THEN (CONV_TAC (RAND_CONV (GEN_PALPHA_CONV "(z1:*,z2:**)"))) THEN (REWRITE_TAC [FST; SND]));; Jim