Hi Thomas, Thanks! Now I got your points:
1. ``(λt. t) = (λt. p)`` cannot reduce to F unless the underlying type
has at least two distinct values (for datatypes with at least two constructors,
it’s easily provable by cases analysis, I think).
2. To prove two lambda-functions, say f and g are not identical, it’s
enough to choose one special value x and shows that f(x) <> g(x). And this fact
depends on theorems but beta-conversion.
Now I think I can resolve both cases.
Regards,
Chun
> Il giorno 04 ago 2017, alle ore 21:38, Thomas Tuerk <tho...@tuerk-brechen.de>
> ha scritto:
>
> Hi Chun,
>
> via a subgoal, you can introduce an assumption for a concrete argument. This
> should be what you need. I'm thinking of something like
>
> First show that a CCS q exists with "q <> p"
> `?q. q <> p` by ...
>
> Then use this new q as an argument)
> `(\t. t) q = (\t. p) q` by PROVE_TAC[]
> Now you are done by BETA reduction and contradicting assumptions.
>
> Best
>
> Thomas
>
>
> On 04.08.2017 20:22, Chun Tian (binghe) wrote:
>> Hi,
>>
>> This is the first time I met the following goal, in which one of the
>> assumptions should be able to reduce to F (then the goal is resolved):
>>
>> R (λt. t)
>> ------------------------------------
>> 4. (λt. t) = (λt. prefix (label l) t)
>>
>> The lambda function has the type of ``CCS -> CCS``, which CCS is my datatype
>> defined by HOL’s Define command. “prefix” is an constructor of CCS
>> datatype. I *know* the equation doesn’t hold, because the whatever input
>> arguments, the resulting CCS on both side must have different “size”, simply
>> because one is the sub-expression of the other. But how can I actually
>> reduce it to F?
>>
>> The other case is a little different:
>>
>> R (λt. t)
>> ------------------------------------
>> 4. (λt. t) = (λt. p)
>>
>> The assumption "(λt. t) = (λt. p)” hold for only one case: when input of
>> lambda function is exactly “p”. For all other cases the left side doesn’t
>> equal to the right side. But from the view of two functions, they’re
>> obviously not identical. But how can I actually reduce it to F?
>>
>> Regards,
>>
>> Chun Tian
>>
>>
>>
>>
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