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 applied_entries_applied_implies_input_state : forall net e, In e (applied_entries (nwState net)) -> applied_implies_input_state (eClient e) (eId e) (eInput e) net.