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[Pierre Casteran <pierre.casteran AT labri.fr>]

muad a écrit :
> > Hello to everyone.
> >
> > This is my context (x: Type)(K: nat -> Type).
> > I would like to know how to rewrite (exists n, K n = x) as (exists m, x =
> > K m).
> >
> > Thanks in advance.
> >     
>
> What is your actual goal and why do you want to do the rewrite.
>   
Hi,


I don't know whether it answers your initial questions, but if you 
consider two logically equivalent
propositions, you can replace one by another in a correct context (see 
documentation on setoids):


Require Import Setoid.
Variables (x: Type)(K: nat -> Type).

Lemma L : (exists m, K m =x) <-> (exists n, x = K n).
split;intros [m H];exists m;auto.
Qed.

Variable P:Prop.
Goal (exists m, K m =x) -> P.
rewrite L.


Admitted.