theorem Th16:
  not M is finite & 0 in N & (N c= M or N in M) implies M*`N = M & N*`M = M
proof
A1: 1*`M = M by CARD_2:21;
  assume not M is finite;
  then
A2: M*`M = M by Th15;
  assume 0 in N;
  then 1 c= N by CARD_2:68;
  then
A3: 1*`M c= N*`M by CARD_2:90;
  assume N c= M or N in M;
  then N*`M c= M*`M by CARD_2:90;
  hence thesis by A2,A3,A1;
end;
