Re: [isabelle] resolve current subgoal with matching premise

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.



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> 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
                    (⋃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



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>:

You could try

    apply ((drule meta_spec)+, erule meta_mp)


    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"


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