(* An example showing that prop-extensionality is incompatible with powerful extensions of the guard condition. This is a variation on the example in subterm2, exploiting missing typing constraints in the commutative cut subterm rule (subterm2 is using the same flaw but for the match rule).  Example due to Cristóbal Camarero on Coq-Club. *)

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