reserve Omega, F for non empty set,
  f for SetSequence of Omega,
  X,A,B for Subset of Omega,
  D for non empty Subset-Family of Omega,
  n,m for Element of NAT,
  h,x,y,z,u,v,Y,I for set;

theorem Th4:
  for n being Nat holds (disjointify(f)).n=f.n \ union rng(f|n)
proof
  let n be Nat;
  (disjointify f).n=disjointify(f,n) by Def4;
  hence thesis;
end;
