reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;
reserve x1,x2,x3,x4,x5,x6,x7,x8 for object;
reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve n,k for Nat;

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;
