Definition Z_to_K (z: Z) :=
  match z with
  | Z0 => 0
  | Zpos _ => n_to_K (Z.abs_nat z)
  | Zneg _ => - (n_to_K (Z.abs_nat z))
  end.

Lemma Z_to_K_pos (z: Z): (0 <= z)%Z -> Z_to_K z = n_to_K (Z.abs_nat z).