Re: [isabelle] Transfer rule for transfer_forall



On 03/11/2013 12:22 PM, Andreas Lochbihler wrote:
Dear all,

I am trying to replace the quotient package (by Cezary and Urban) with
lifting and transfer for the theory TLList in AFP-Coinductive. When I
invoke transfer on the new coinduction rule for tllist_all2 (see below),
the second subgoal is

"Transfer.Rel
      (((cr_tllist ===> cr_tllist ===> op =) ===> op =) ===> op =) ?a76
      transfer_forall"

and the first one is cluttered with transfer_forall and
transfer_implies. Can anyone knowledgable please help me in figuring out
what ?a76 should be? I hope that there's a canonical solution. I can
also try to produce a smaller example but have failed so far.

lemma tllist_all2_coinduct:
   assumes "X xs ys"
   and "!!xs ys. X xs ys ==>
   (is_TNil xs = is_TNil ys) &
   (is_TNil xs --> is_TNil ys --> R (terminal xs) (terminal ys)) &
   (~ is_TNil xs --> ~ is_TNil ys
    --> P (thd xs) (thd ys) &
        (X (ttl xs) (ttl ys) | tllist_all2 P R (ttl xs) (ttl ys)))"
   shows "tllist_all2 P R xs ys"
using assms
apply transfer


Some more data on the setup:

definition cr_tllist :: "('a llist * 'b) => ('a, 'b) tllist => bool"
   where "cr_tllist = (%(xs, b) ys. tllist_of_llist b xs = ys)"

lemma Quotient_tllist:
   "Quotient (%(xs, a) (ys, b). xs = ys & (lfinite ys --> a = b))
      (%(xs, a). tllist_of_llist a xs)
      (%ys. (llist_of_tllist ys, terminal ys))
      cr_tllist"

lemma reflp_tllist:
   "reflp (%(xs, a) (ys, b). xs = ys & (lfinite ys --> a = b))"

setup_lifting (no_code) Quotient_tllist reflp_tllist

Thanks in advance for any pointers,
Andreas


I'll take a look at it. Could please send me a self-contained file? Thanks.

Ondrej




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