
theorem
  for a, b being Ordinal st 1 in a & a in b holds b +^ a in a *^ b
proof
  let a, b be Ordinal;
  assume A1: 1 in a & a in b;
  then A2: 2 *^ b c= a *^ b by Lm2, ORDINAL1:21, ORDINAL2:41;
  b +^ a in b +^ b by A1, ORDINAL2:32;
  then b +^ a in 2 *^ b by Th2;
  hence thesis by A2;
end;
