
theorem
  for a, b, c being Ordinal st b c= c holds a (+) b c= a (+) c
proof
  let a, b, c be Ordinal;
  assume A1: b c= c;
  per cases by ORDINAL1:16;
  suppose c c= b;
    hence thesis by A1, XBOOLE_0:def 10;
  end;
  suppose b in c;
    hence thesis by Th107, ORDINAL1:def 2;
  end;
end;
