theorem Th31:
  for X, Y be RealNormSpace holds (the carrier of X) --> 0.Y = 0.
  R_NormSpace_of_BoundedLinearOperators(X,Y)
proof
  let X, Y be RealNormSpace;
  ((the carrier of X) --> 0.Y) =0.R_VectorSpace_of_BoundedLinearOperators(
  X,Y) by Th26
    .=0.R_NormSpace_of_BoundedLinearOperators(X,Y);
  hence thesis;
end;
