Remark xelements_empty:
    forall (A: Type) (m: t A) i, (forall i, get i m = None) -> xelements m i nil = nil.

Theorem elements_canonical_order: forall (A B: Type) (R: A -> B -> Prop) (m: t A) (n: t B), (forall i x, get i m = Some x -> exists y, get i n = Some y /\ R x y) -> (forall i y, get i n = Some y -> exists x, get i m = Some x /\ R x y) -> list_forall2 (fun i_x i_y => fst i_x = fst i_y /\ R (snd i_x) (snd i_y)) (elements m) (elements n).