theorem
  N <> 0 implies M c= M*`N & M c= N*`M
proof
  assume
A1: N <> 0;
A2: card M = M;
  card N = N;
  then
A3: M*`N = card ( M *^ N) by A2,Th13;
  M c= M *^ N by A1,ORDINAL3:36;
  hence thesis by A2,A3,CARD_1:11;
end;
