Fixpoint app (a b: L) {struct a}: L :=
    match a with
    | one x => cons x b
    | cons x y => cons x (app y b)
    end.Definition head := match l with one x => x | cons x _ => x end.Definition tail := match l with one _ => List.nil | cons _ x => to_plain x end.

(* Specifications: *)
Lemma head_in_self: List.In head l.
Lemma In_sound x: List.In x l -> (head = x \/ List.In x tail).
Lemma In_cons_head (x: T) y: List.In x (cons x y).
Lemma In_one (x: T): List.In x (one x).
Lemma coerced_cons_eq (h: T): List.cons h l = cons h l.