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

Theorem ghost_simulation_1 :
forall net net' failed failed' out,
@step_failure _ _ refined_failure_params (failed, net) (failed', net') out ->
@step_failure _ _ failure_params (failed, deghost net) (failed', deghost net') out.