Proof using rri.
intros.
find_eapply_lem_hyp msg_lift_prop; eauto.
find_eapply_lem_hyp lift_prop; eauto.
Qed.

Theorem lower_prop_all_the_way :
forall P : _ -> Prop,
(forall (net : @network _ raft_msg_refined_multi_params), msg_refined_raft_intermediate_reachable net -> P (deghost (mgv_deghost net))) ->
(forall net, raft_intermediate_reachable net -> P net).