File: proofirrelevance.v

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(* This was working in version 8.1beta (bug in the Sort-polymorphism
   of inductive types), but this is inconsistent with classical logic 
   in Prop *)

Inductive bool_in_prop : Type := hide : bool -> bool_in_prop
with bool : Type := true : bool | false : bool.

Lemma not_proof_irrelevance : ~ forall (P:Prop) (p p':P), p=p'.
intro H; pose proof (H bool_in_prop (hide true) (hide false)); discriminate.
Qed.