Re: [isabelle] resolve current subgoal with matching premise



Never mind my second question.

Local_Theory.note together with @{attributes [a]} works as expected after I fixed a typo in my "a" (which was slightly longer in my real example).

cheers

chris

On 12/05/2014 04:09 PM, Peter Lammich wrote:
On Fr, 2014-12-05 at 15:49 +0100, Dmitriy Traytel wrote:
Well, the Subgoal.FOCUS combinator gives one at least some structure
(fixes and assumes) in the hands.

So try:

apply (tactic ‹HEADGOAL (Subgoal.FOCUS (fn {prems, ...} => HEADGOAL
(resolve_tac prems)) @{context})›)

I believe Peter's solution is similar (but using CSUBGOAL instead).

It does. I have copied it from the implementation of the
"assumption"-method.
Correct handling of schematics was important in my use-case
(program synthesis, involving recursion-combinator), thus I could not
use FOCUS.

--
   Peter




Dmitriy

On 05.12.2014 15:30, Lawrence Paulson wrote:
I don’t know how to generate structured proofs by a package.  I assume that it would be necessary to generate calls to the underlying abstract machine.  I am not aware that this has been done before.

Larry Paulson


On 5 Dec 2014, at 14:24, Christian Sternagel <c.sternagel at gmail.com> wrote:

For a manual proof in Isar I completely agree. However, this is just a single example of many that are automatically generated inside a package. And the tactic should work for all generated goals (whose shape depends on the underlying datatype). For making the tactic structured - also I might be wrong since I never tried very hard - it seemed that I would have to do a lot of awkward code about how many premises and IHs are there and at what positions do they fit together etc. I had at least the feeling that such things should be left to some automatic search. But of course I would be delighted to be convinced otherwise.

cheers

chris

On 12/05/2014 03:09 PM, Lawrence Paulson wrote:
In this sort of situation, I would make every effort to switch to a structured proof style, when the induction hypothesis could be applied as an ordinary rule using the most primitive methods.

Larry Paulson


On 5 Dec 2014, at 09:40, Christian Sternagel <c.sternagel at gmail.com> wrote:

Thanks for the hint Jasmin!

your suggestion looks promising, but unfortunately the last "erule meta_mp" fails on my actual subgoal, which looks as follows:

goal (1 subgoal):
1. ⋀x1a x2a p y z x ya yb xa xb yc.
        (⋀x2aa x2aaa x2aaaa x2aaaaa.
            x2aa ∈ set_tree x2a ⟹
            x2aaa ∈ Basic_BNFs.fsts x2aa ⟹
            x2aaaa ∈ set x2aaa ⟹
            x2aaaaa ∈ set_tree x2aaaa ⟹
            (⋀y. y ∈ set_nested x2aaaaa ⟹ show_law s y) ⟹
            show_law (showsp_nested s) x2aaaaa) ⟹
        (⋀y. y ∈ insert x1a
                   (UNION
                     (⋃x∈set_tree x2a.
                         ⋃x∈Basic_BNFs.fsts x.
                            UNION (set x) set_tree)
                     set_nested) ⟹
              show_law s y) ⟹
        yb ∈ set_tree x2a ⟹
        xa ∈ Basic_BNFs.fsts yb ⟹
        xb ∈ set xa ⟹
        yc ∈ set_tree xb ⟹ show_law (showsp_nested s) yc

cheers

chris

On 12/04/2014 10:39 PM, Jasmin Christian Blanchette wrote:
Am 04.12.2014 um 22:37 schrieb Jasmin Christian Blanchette <jasmin.blanchette at gmail.com>:

You could try

     apply ((drule meta_spec)+, erule meta_mp)

E.g.:

     lemma "!! a1 aJ aN.
      (!! b1 bK. q b1 bK) ==>
      (!! i1 iI iM. r i1 iI iM ==> P iI) ==>
      (!! z1 zL. s z1 zL) ==> P aJ"
     apply ((drule meta_spec)+, erule meta_mp)
I forgot: The example looks more impressive if you add

      consts P :: "nat ⇒ bool"
      consts q :: "nat ⇒ nat ⇒ bool"
      consts r :: "nat ⇒ nat ⇒ nat ⇒ bool"
      consts s :: "nat ⇒ nat ⇒ bool"

Jasmin











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