(* An example showing that prop-extensionality is incompatible with powerful extensions of the guard condition. Unlike the example in guard2, it is not exploiting the fact that the elimination of False always produces a subterm.  Example due to Cristobal Camarero on Coq-Club. Adapted to nested types by Bruno Barras. *)

Axiom prop_ext: forall P Q, (P<->Q)->P=Q.