Record has_fixpoint (A:Prop) : Prop :=
  {F : (A -> A) -> A; Fix : forall f:A -> A, F f = f (F f)}.Record has_fixpoint (A:Prop) : Prop :=
  {F : (A -> A) -> A; Fix : forall f:A -> A, F f = f (F f)}.Record has_fixpoint (A:Prop) : Prop :=
  {F : (A -> A) -> A; Fix : forall f:A -> A, F f = f (F f)}.

Lemma ext_prop_fixpoint : prop_extensionality -> forall A:Prop, inhabited A -> has_fixpoint A.