
theorem
  for a, b being Ordinal st 1 in a & a in b holds a *^ b in exp(b,a)
proof
  let a, b be Ordinal;
  assume A1: 1 in a & a in b; then
  A3: exp(b,2) c= exp(b,a) by Lm2, ORDINAL1:21, ORDINAL4:27;
  a *^ b in b *^ b by A1, ORDINAL2:40;
  then a *^ b in exp(b,2) by Th4;
  hence thesis by A3;
end;
