Proof using.
intuition.
unfold key_in_output_list in *.
break_exists; intuition.
Qed.

(* Specifications: *)
Lemma doLeader_key_in_output_list :
forall st h out st' m client id,
doLeader st h = (out, st', m) ->
~ key_in_output_list client id out.
Lemma doLeader_key_in_output_list :
forall st h out st' m,
doLeader st h = (out, st', m) ->
~ key_in_output_list client id out.