theorem Th17:
  not M is finite & (N c= M or N in M) implies M*`N c= M & N*`M c= M
proof
  assume not M is finite & (N c= M or N in M);
  then M*`N = M or not 0 in N by Th16;
  then M*`N c= M or N = 0 & M*`0 = 0 & 0 c= M
  by CARD_2:20,ORDINAL3:8;
  hence thesis;
end;
