
theorem Th99:
  for a, b being Ordinal holds a c= a (+) b
proof
  let a, b be Ordinal;
  set E1 = omega -exponent CantorNF a, E2 = omega -exponent CantorNF b;
  A1: dom CantorNF a c= dom CantorNF(a(+)b) by Th77;
  for x being object st x in dom CantorNF a
    holds (CantorNF a).x c= (CantorNF(a(+)b)).x by Th98;
  then Sum^ CantorNF a c= Sum^ CantorNF(a(+)b) by A1, Th28;
  hence thesis;
end;
