Proof using.
induction l; intros; simpl; repeat break_match; subst; eauto.
Qed.

(* Specifications: *)
Lemma acknowledge_all_ops_func_target_ext :
forall l t t',
(forall k, In (IRU k) t -> In (IRU k) t') ->
(forall k, In (IRU k) t' -> In (IRU k) t) ->
acknowledge_all_ops_func l t = acknowledge_all_ops_func l t'.