Definition input_correct (tr : list (name * (raft_input + list raft_output))) : Prop :=
    (forall client id i i' h h',
       In (h, inl (ClientRequest client id i)) tr ->
       In (h', inl (ClientRequest client id i')) tr ->
       i = i').

Lemma get_output_in_output_trace : forall tr client id o, get_output tr (client, id) = Some o -> in_output_trace client id o tr.