Proof with eauto using subseq_uniqueIndices, removeAfterIndex_subseq.
intros...
Qed.

(* Specifications: *)
Lemma maxIndex_subset :
forall xs ys,
sorted xs -> sorted ys ->
(forall x, In x xs -> In x ys) ->
maxIndex xs <= maxIndex (orig_base_params:=orig_base_params) ys.