reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace;
reserve x,y for Point of X;
reserve A, B for Subset of X;
reserve P, Q for Subset of X;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace,
  Y0 for non empty SubSpace of X;

theorem
  for x being Point of Y holds Sspace(x) is SubSpace of MaxADSspace(x)
proof
  let x be Point of Y;
A1: the carrier of Sspace(x) = {x} by TEX_2:def 2;
  the carrier of MaxADSspace(x) = MaxADSet(x) by Def17;
  hence thesis by A1,Lm2,Th12;
end;
