reserve X,Y,Z,x,y,y1,y2 for set,
  D for non empty set,
  k,n,n1,n2,m2,m1 for Nat,

  L,K,M,N for Cardinal,
  f,g for Function;
reserve r for Real;
reserve p,q for FinSequence,
  k,m,n,n1,n2,n3 for Nat;
reserve f,f1,f2 for Function,
  X1,X2 for set;

theorem
  X <> {} & X is finite & not Y is finite implies card Y *` card X = card Y
proof
  assume that
A1: X <> {} & X is finite and
A2: not Y is finite;
  card X in card Y & 0 in card X by A1,A2,CARD_3:86,ORDINAL3:8;
  hence thesis by A2,Th16;
end;
