Example undecidable_predicate_with_the_minimization_property :
    Minimization_Property P.Local Notation representative_boolean_partition :=
  (forall R:bool->bool->Prop,
    Equivalence R -> exists f, forall x, R x (f x) /\ forall y, R x y -> f x = f y).

(* Specifications: *)
Theorem representative_boolean_partition_imp_excluded_middle : representative_boolean_partition -> excluded_middle.
Theorem excluded_middle_imp_representative_boolean_partition : excluded_middle -> representative_boolean_partition.
Theorem excluded_middle_iff_representative_boolean_partition : excluded_middle <-> representative_boolean_partition.