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 A being non empty Subset of Y holds Sspace(A) is SubSpace of
  MaxADSspace(A)
proof
  let A be non empty Subset of Y;
A1: the carrier of Sspace(A) = A by Lm3;
  the carrier of MaxADSspace(A) = MaxADSet(A) by Def18;
  hence thesis by A1,Lm2,Th32;
end;
