theorem Th74:
  not M is finite implies M+`M = M
proof
  assume not M is finite;
  then M*^succ 1 = M by Th72;
  then card M = (card 2)*`card M by Th13
    .= card (succ 1*^ M) by Th13
    .= card (1*^ M+^ M) by ORDINAL2:36
    .= M+`M by ORDINAL2:39;
  hence thesis;
end;
