Proof using.
elim => //.
move => tr l IH.
rewrite /= IH.
break_let.
break_match => //.
by rewrite map_id.
Qed.

Theorem mgv_ghost_simulation_1 :
forall net net' failed failed' out,
@step_failure _ _ mgv_refined_failure_params (failed, net) (failed', net') out ->
@step_failure _ _ failure_params (failed, mgv_deghost net) (failed', mgv_deghost net') out.