Definition everything (net : ghost_log_network) : Prop :=
    lifted_maxIndex_sanity net /\
    commit_invariant net /\
    state_machine_safety (deghost (mgv_deghost net)).

Lemma directly_committed_state_same : forall net net' e, (forall h, nwState net' h = nwState net h) -> directly_committed net e -> directly_committed net' e.