Sorry Michael I cut and pasted the wrong goal for some reason. Here is the
corrected one:
scf (A :mor -> bool) A (λ(x :mor). x) c sce A (a :mor) =
sce A ((λ(x :mor). x) a)
------------------------------------
0. homset (A :mor -> bool)
4. (A :mor -> bool) (a :mor)
It doesn't depend on scr. I also found out that writing out in this non
beta-reduced form I can solve it with irule SC_EV >> asm_simp_tac bool_ss
[], but not in the beta reduced form. metis_tac and prove_tac still fails
on both (beta-reduced or not reduced).
Sorry for the confusion.
Haitao
On Tue, Mar 5, 2019 at 10:07 PM <michael.norr...@data61.csiro.au> wrote:
> What did simp[FUNSET_ID, SC_EV] do to this goal, if anything?
>
>
>
> I’d expect it to change the goal to
>
>
>
> sce A a = scr A c sce A a
>
>
>
> (You haven’t shown us any assumptions/theorems about scr.)
>
>
>
> Michael
>
>
>
> *From: *Haitao Zhang <zhtp...@gmail.com>
> *Date: *Wednesday, 6 March 2019 at 16:57
> *To: *hol-info <hol-info@lists.sourceforge.net>
> *Subject: *[Hol-info] HOL difficulty with this subgoal
>
>
>
> I had great difficulty to have HOL prove the following subgoal (I turned
> on typing for debugging, ``$c`` is a composition operator like ``$o``):
>
>
>
> scf (A :mor -> bool) A (λ(x :mor). x) c sce A (a :mor) = scr A c sce A a
> ------------------------------------
> 0. homset (A :mor -> bool)
> 4. (A :mor -> bool) (a :mor)
>
>
>
> Which should be directly derived from two theorems below and assumptions
> 0,4 (I removed other ones to reduce clutter) :
>
>
>
> > FUNSET_ID;
> val it = ⊢ ∀(A :α -> bool). FUNSET A A (λ(x :α). x): thm
>
> > SC_EV;
> val it =
> ⊢ ∀(A :mor -> bool) (B :mor -> bool) (f :mor -> mor) (a :mor).
> homset A ⇒
> homset B ⇒
> FUNSET A B f ⇒
> A a ⇒
> (scf A B f c sce A a = sce B (f a)): thm
>
>
>
> Eventually I need to manually instantiate everything to solve it:
>
>
>
> > e (mp_tac (BETA_RULE (MATCH_MP ((UNDISCH o UNDISCH o SPEC ``a:mor`` o
> SPEC ``\x.(x:mor)`` o Q.SPEC `A` o Q.SPEC `A`) SC_EV) (ISPEC
> ``A:mor->bool`` FUNSET_ID))) >> asm_simp_tac bool_ss []);
>
>
>
> It seems the main obstacle was "ground const vs. polymorphic const" based
> on the error messages I got during various trials. It was important that I
> spelled out all type correctly for it to work.
>
>
>
> Haitao
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