Set Implicit Arguments.
Require U.
Require qs_parts.
Require NDP.
Require vec.
Arguments length {A}.
Arguments fst {A} {B}.
Section contents.
Variables (ee: E) (ol: list ee).

Lemma simpler_same_values l d c:
proj1_sig (simplerPartition ee (subscript d) (map (subscript (T:=ee) (ol:=ol)) l)) c =
map (subscript (T:=ee) (ol:=ol)) (proj1_sig (simplerPartition (UE ee ol) d l) c).