Generalizable All Variables.
Fixpoint removeV `{eqDecV : @EqDec V eqV equivV}`(x : V) (l : list V) : list V
:=
match l with
| nil => nil
| y::tl => if (equiv_dec x y) then removeV x tl else y::(removeV x tl)
end.

Lemma remove_le {V:Type}{eqV:relation V}{equivV:@Equivalence V eqV}{eqDecV :
@EqDec V eqV equivV} (xs : list V) (x : V) :
length (removeV x xs) < length (x :: xs).