*To*: Christian Sternagel <c.sternagel at gmail.com>*Subject*: Re: [isabelle] resolve current subgoal with matching premise*From*: Lawrence Paulson <lp15 at cam.ac.uk>*Date*: Fri, 5 Dec 2014 14:30:47 +0000*Cc*: "cl-isabelle-users at lists.cam.ac.uk" <cl-isabelle-users at lists.cam.ac.uk>*In-reply-to*: <5481C032.4000405@gmail.com>*References*: <5480CDAE.4090307@gmail.com> <94C2957A-B4C7-42ED-B349-3F3C8F583730@in.tum.de> <5B9C47B8-4C4C-4762-80BB-15BBA02D90A5@gmail.com> <54817D7F.1020704@gmail.com> <C381B664-9A9A-4131-9620-0D0481E41233@cam.ac.uk> <5481C032.4000405@gmail.com>

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 >>>> >>> >>

**Follow-Ups**:**Re: [isabelle] resolve current subgoal with matching premise***From:*Dmitriy Traytel

**References**:**[isabelle] resolve current subgoal with matching premise***From:*Christian Sternagel

**Re: [isabelle] resolve current subgoal with matching premise***From:*Jasmin Christian Blanchette

**Re: [isabelle] resolve current subgoal with matching premise***From:*Jasmin Christian Blanchette

**Re: [isabelle] resolve current subgoal with matching premise***From:*Christian Sternagel

**Re: [isabelle] resolve current subgoal with matching premise***From:*Lawrence Paulson

**Re: [isabelle] resolve current subgoal with matching premise***From:*Christian Sternagel

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