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 Th17:
  for X being set st X c= u holds X is Element of SubstLatt (V, C)
proof
  let X be set;
  reconsider u9 = u as Element of SubstitutionSet (V, C) by SUBSTLAT:def 4;
  assume X c= u;
  then X c= u9;
  then X in SubstitutionSet (V, C) by Lm4;
  hence thesis by SUBSTLAT:def 4;
end;
