
theorem
  for c, d, e being Cantor-component Ordinal
  st omega -exponent d in omega -exponent c &
    omega -exponent e in omega -exponent d
  holds <% c, d, e %> is Cantor-normal-form
proof
  let c, d, e be Cantor-component Ordinal;
  assume that
    A1: omega -exponent d in omega -exponent c and
    A2: omega -exponent e in omega -exponent d;
  A3: <% d, e %> is Cantor-normal-form by A2, Th35;
  omega -exponent(<%d,e%>.0) in omega -exponent last({}^<%c%>)
    by A1, AFINSQ_1:92;
  then <%c%>^<%d,e%> is Cantor-normal-form by A3, Th33;
  hence thesis by AFINSQ_1:37;
end;
