Section Undup.
Variable X : eqType.
Implicit Types A B : list X.
Fixpoint undup A : list X :=
match A with
| nil => nil
| x::A' => if decision (x el A') then undup A' else  x :: undup A'
end.

Lemma rep_in x A U :
A <<= U -> x el A -> x el rep A U.