
theorem Th59:
  for c being Cantor-component Ordinal
  holds c = (omega -leading_coeff c) *^ exp(omega, omega -exponent c)
proof
  let c be Cantor-component Ordinal;
  consider b being Ordinal, n being Nat such that
    A1: 0 in Segm n & c = n*^exp(omega,b) by ORDINAL5:def 9;
  A2: omega -leading_coeff c = n by A1, Th57, ORDINAL1:def 12;
  0 in n & n in omega by A1, ORDINAL1:def 12;
  hence thesis by A1, A2, ORDINAL5:58;
end;
