Definition move_forward {A}(i j:nat)(l:list A)(d:A) : list A :=
  firstn i l ++ firstn j (skipn (S i) l) ++ (nth i l d :: skipn (S (i+j)) l).

Lemma length_move_forward : forall A i j (l:list A) d, i+j < length l -> length (move_forward i j l d) = length l.