Proof using taifoli rri.
intros.
pose proof (lift_prop _ terms_and_indices_from_one_log_invariant).
unfold terms_and_indices_from_one_log in *.
rewrite <- deghost_spec with (net0 := net). auto.
Qed.

Lemma doLeader_preserves_committed :
forall (net net' : ghost_log_network) d h os d' ms gd  e t,
doLeader d h = (os, d', ms) ->
nwState net h = (gd, d) ->
(forall h', nwState net' h' = update name_eq_dec (nwState net) h (gd, d') h') ->
lifted_committed net e t ->
lifted_committed net' e t.