(** Thanks to the axiom of choice, the boolean witnesses move from the propositional world to the relevant world *)

(* Specifications: *)
Theorem proof_irrel_rel_choice_imp_eq_dec : a1=a2 \/ ~a1=a2.
(** An alternative more concise proof can be done by directly using the guarded relational choice *)
Lemma proof_irrel_rel_choice_imp_eq_dec' : a1=a2 \/ ~a1=a2.
End ProofIrrel_RelChoice_imp_EqEM.