
theorem Th2:
  for V being RealUnitarySpace, W being Subspace of V, x being object
  st x in W holds x in V
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let x be object;
  assume x in W;
  then
A1: x in the carrier of W;
  the carrier of W c= the carrier of V by Def1;
  hence thesis by A1;
end;
