Definition restrict_code (m : list A) (c : code A) : 
  code A :=
  map (fun x => (fst x, find_code eqA_dec (fst x) c))
    (frequency_list eqA_dec m).

Theorem restrict_code_encode_length : forall (m : list A) (c : code A), encode eqA_dec c m = encode eqA_dec (restrict_code m c) m.