
theorem Th55:
  for a, b being Ordinal st a in b holds b -leading_coeff a = a
proof
  let a, b be Ordinal;
  assume A1: a in b;
  per cases;
  suppose 0 in a;
    thus b -leading_coeff a = a div^ exp(b, 0) by A1, Th21
      .= a div^ 1 by ORDINAL2:43
      .= a by ORDINAL3:71;
  end;
  suppose not 0 in a;
    then a = 0 or a in 0 by ORDINAL1:14;
    hence thesis by ORDINAL3:70;
  end;
end;
