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[Coq-Club] Excluded Middle for Type?


Chronological Thread 
  • From: Chris Casinghino <chris.casinghino AT gmail.com>
  • To: Coq Club <coq-club AT inria.fr>
  • Subject: [Coq-Club] Excluded Middle for Type?
  • Date: Tue, 2 Jul 2013 15:38:03 -0400

Hi all,

I notice that, where the Coq FAQ discusses safe axioms, it mentions
excluded middle only for "Prop". This also seems to be the case in
the standard libraries.

Would it also be safe to add excluded middle for "Type"? That is,
could I add the following?

Inductive sum (A B : Type) : Type :=
| leftT : A -> sum A B
| rightT : B -> sum A B.

Axiom em_type : forall A : Type, sum A (A -> False).

Thanks!

--Chris Casinghino



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