reserve V, C, x, a, b for set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve C for finite set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve u, v for Element of SubstLatt (V, C);
reserve s, t, a, b for Element of PFuncs (V,C);
reserve K, L for Element of SubstitutionSet (V, C);

theorem Th20:
  (diff u).v [= u
proof
  (diff u).v = u \ v by Def7;
  then for a be set st a in (diff u).v ex b be set st b in u & b c= a;
  hence thesis by Lm8;
end;
