From : Maxime Dénès <mail AT maximedenes.fr>

: Maxime Dénès <mail AT maximedenes.fr> To : coq-club AT inria.fr

: coq-club AT inria.fr Subject : [Coq-Club] Propositional extensionality is inconsistent in Coq

: [Coq-Club] Propositional extensionality is inconsistent in Coq Date: Thu, 12 Dec 2013 16:41:18 -0500

Hi folks,Arthur and I refined Daniel's example to show that Propositional Extensionality (even the weaker version of it) as defined in Coq's standard library is inconsistent in Coq's current theory:---------------------------------------------Require Import ClassicalFacts.Section func_unit_discr.Hypothesis Heq : (False -> False) = True.Fixpoint contradiction (u : True) : False :=contradiction (match Heq in (_ = T) return T with| eq_refl => fun f:False => match f with endend).End func_unit_discr.Lemma foo : provable_prop_extensionality -> False.Proof.intro; apply contradiction.apply H.trivial.trivial.Qed.Print Assumptions foo.Print provable_prop_extensionality.---------------------------------------------(Typechecked with Coq 8.4pl2).Was that fact known?Maxime.