reserve            x for object,
               X,Y,Z for set,
         i,j,k,l,m,n for Nat,
                 r,s for Real,
                  no for Element of OrderedNAT,
                   A for Subset of [:NAT,NAT:];

theorem Th2:
  Z c= X & X \ Z is finite implies
  ex W being finite Subset of X st X \ W = Z
  proof
    assume that
A1: Z c= X and
A2: X \ Z is finite;
    X \ (X \ Z) = X /\ Z by XBOOLE_1:48
               .= Z by A1,XBOOLE_1:17,XBOOLE_1:19;
    hence thesis by A2;
  end;
