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Re: [Coq-Club] Tactics to manipulate real arithmetic (w/o solving)


Chronological Thread 
  • From: Laurent Thery <Laurent.Thery AT inria.fr>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] Tactics to manipulate real arithmetic (w/o solving)
  • Date: Wed, 15 Mar 2017 10:14:56 +0100


Hi,

a while ago, I have been interested in having Coq tactics to perform "human" simplifications (the idea was to follow closely paper proofs via tactics : pols would simplify polr would rewrite with = and <= and polf would factorize)

Incredibly enough the code is still compiling in 8.6 so I put it here

https://github.com/thery/PolTac

the idea behind the code is explained in this note

https://hal.inria.fr/inria-00070394

> 1) allow rewriting with equations/inequations where the term to be
> rewritten is not immediately found, but can be isolated:
>

you get rewrting modulo AC with polr so

polr H should work


Example e2 (a b c : R) : exists (x : R), a * b * c = b * x * a.
(* figure out that you should instantiate x with c *)

I would have thought that

eexists; pols; apply refl_equal

would do the job

Unfortunately, the code was written before evar came into fashion, so it does not support it but I'll look into it

--
Laurent




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