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 Th1:
  for W being finite Subset of X st X \ W c= Z holds
    X \ Z is finite
  proof
    let W be finite Subset of X;
    assume X \ W c= Z;
    then X \ Z c= (X \ (X \ W)) by XBOOLE_1:34;
    then X \ Z c= X /\ W by XBOOLE_1:48;
    hence thesis;
  end;
