Thanks qspecl_then and friends are great! Sometimes it is easier to be more specific.
Haitao On Wed, Mar 6, 2019 at 1:46 AM <michael.norr...@data61.csiro.au> wrote: > If you really need to instantiate a theorem by hand, using Q.SPEC_THEN and > Q.ISPEC_THEN is usually better. The first is also available under the name > qspec_then. > > > > E.g., you can do > > > > qspec_then `a` mp_tac mytheorem > > > > If you need to do lots of specialisations you can use the list forms: > > > > qspecl_then [`a`, `b`, `c`] mp_tac mytheorem > > > > If you want to specialise an assumption (rather than mytheorem), use > first_x_assum or similar to pull that assumption out of the assumptions: > > > > first_x_assum (qspecl_then [`a+6`, `f b`] mp_tac) > > > > The big advantage of Q.SPEC_THEN and friends is that the arguments are > parsed in the context of the goal (so something like `f b` above will > ensure that f and b get the right types rather than `’a->’b` and `’a`). > > > > Michael > > > > *From: *Haitao Zhang <zhtp...@gmail.com> > *Date: *Wednesday, 6 March 2019 at 18:42 > *To: *"Norrish, Michael (Data61, Acton)" <michael.norr...@data61.csiro.au> > *Cc: *hol-info <hol-info@lists.sourceforge.net> > *Subject: *Re: [Hol-info] HOL difficulty with this subgoal > > > > I should also add that simp [..] would take a step in the wrong direction > as I have an equality on the assumptions list that I used earlier in the > other direction (through SYM). simp_tac does not do anything as assumptions > are required. And as I can see now the step does not actually depend on > FUNSET_ID as there is already a fact proved using it in the assumptions. I > was using FUNSET_ID in the earlier solution because I was manually > instantiating the antecedent (instead of searching for it among the > assumptions). > > > > Haitao > > > > > > On Tue, Mar 5, 2019 at 11:30 PM Haitao Zhang <zhtp...@gmail.com> wrote: > > 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 > > _______________________________________________ > hol-info mailing list > hol-info@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/hol-info > > _______________________________________________ > hol-info mailing list > hol-info@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/hol-info >
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