
theorem
  for V being strict RealUnitarySpace, W being strict Subspace of V st
  the carrier of W = the carrier of V holds W = V
proof
  let V be strict RealUnitarySpace;
  let W be strict Subspace of V;
  assume
A1: the carrier of W = the carrier of V;
  V is Subspace of V by Th19;
  hence thesis by A1,Th24;
end;
