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[Coq-Club] Pointwise definition of function


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  • From: Anton Podkopaev <anton AT podkopaev.net>
  • To: coq-club AT inria.fr
  • Subject: [Coq-Club] Pointwise definition of function
  • Date: Wed, 15 Aug 2018 16:19:43 +0300
  • Authentication-results: mail2-smtp-roc.national.inria.fr; spf=None smtp.pra=anton AT podkopaev.net; spf=Pass smtp.mailfrom=anton AT podkopaev.net; spf=None smtp.helo=postmaster AT forward106j.mail.yandex.net
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Hello,

I'm trying to define a function pointwise. To do so, I'd like to prove the following lemma:

Definition pointwise_func_def {A B} (P : B -> Prop)
      (H : forall (n : A), exists fn, P fn) :
  exists (f : A -> B), forall n, P (f n).

I think that it can't be proven w/o additional axioms.
Do you know how to prove the lemma?

thank you,
Anton Podkopaev



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