Fixpoint force_lengthn {A} n (xs: list A) (default: A) :=
  match n, xs with
  | O, _ => nil
  | S n0, nil => default :: force_lengthn n0 nil default
  | S n0, hd :: tl => hd :: force_lengthn n0 tl default
  end.

Lemma force_lengthn_id: forall {A} n ct (d: A), length ct = n -> force_lengthn n ct d = ct.