
theorem ADI:
  for a be non zero Integer holds  a/(Parity a) = a div (Parity a)
  proof
    let a be non zero Integer;
    (Parity a) > 0 & Parity a divides a by Th3; then
    A1: a mod (Parity a) = 0 by INT_1:62;
    a/(Parity a) = ((a div (Parity a))*(Parity a) +
      (a mod (Parity a)))/(Parity a) by INT_1:59
    .= ((a div (Parity a))*(Parity a))/(Parity a) by A1;
    hence thesis by XCMPLX_1:89;
  end;
