Definition contiguous_range_exact_lo xs lo :=
    (forall i,
       lo < i <= maxIndex xs ->
       exists e,
         eIndex e = i /\
         In e xs) /\
    (forall e,
       In e xs ->
       lo < eIndex e).

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.