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RE: [Coq-Club] Proof irrelevance for equalities - is there a trick without axioms?


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  • From: "Soegtrop, Michael" <michael.soegtrop AT intel.com>
  • To: "coq-club AT inria.fr" <coq-club AT inria.fr>
  • Subject: RE: [Coq-Club] Proof irrelevance for equalities - is there a trick without axioms?
  • Date: Wed, 17 Aug 2016 19:03:50 +0000
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Dear Jason, Jonathan,

thanks for the solution and explanation.

I experimented a bit. I think that this works for any literal term of any
type, even if it doesn't have decidable equality. E.g.:

Open Scope list_scope.

Lemma TestNatList: forall (T : Type) (feq : 3::nil=3::nil->T) (H1 :
3::nil=3::nil), feq eq_refl = feq H1.
Proof.
intros.
refine (match H1 with
| eq_refl _ => _
end).
reflexivity.
Qed.

The resulting proof term is lengthy. I guess the decidable equality is
required if the value compared is not a literal, but a parameter.

Best regards,

Michael
Intel Deutschland GmbH
Registered Address: Am Campeon 10-12, 85579 Neubiberg, Germany
Tel: +49 89 99 8853-0, www.intel.de
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