Definition pos_el (X : eqType) (x : X) (A : list X) (H : x el A) := proj1_sig (pos_el' H).
Definition index (X : finType) (x : X) := pos_el (elem_spec x).

Lemma pos_inj (X : eqType) (x y : X) (A : list X) n :
pos x A = Some n -> pos y A = Some n -> x = y.