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;
