Proof using.
elim => //=.
move => o out IH to.
by case pt_map_output => [o'|]; rewrite IH.
Qed.

(* Specifications: *)
Theorem step_ordered_pt_mapped_simulation_1 :
forall net net' tr,
@step_ordered _ multi_fst net net' tr ->
@step_ordered _ multi_snd (pt_map_onet net) (pt_map_onet net') (filterMap pt_map_trace_ev tr) \/
pt_map_onet net' = pt_map_onet net /\ filterMap pt_map_trace_ev tr = [].