theorem
  for V being strict RealLinearSpace, W being strict Subspace of V holds
  the carrier of W = the carrier of V implies W = V
proof
  let V be strict RealLinearSpace, W be strict Subspace of V;
  assume
A1: the carrier of W = the carrier of V;
  V is Subspace of V by Th25;
  hence thesis by A1,Th30;
end;
