Proof using pt_map_msg_injective.
elim => //=.
move => m0 l IH.
move => m1 m2 H_eq H_in.
have IH' := IH _ _ H_eq.
break_match; last first.
right.
exact: IH'.
have IH'' := IH _ _ Heqo.
case: H_in => H_in; last first.
right.
exact: IH'.
rewrite H_in in IH'' Heqo.
left.
move: Heqo H_eq.
exact: pt_map_msg_injective.
Qed.

(* Specifications: *)
Lemma in_all_before_pt_map_msg :
forall l m0 m1 m'0 m'1,
pt_map_msg m0 = Some m'0 ->
pt_map_msg m1 = Some m'1 ->
before_all m'0 m'1 (filterMap pt_map_msg l) ->
before_all m0 m1 l.