theorem Th26:
  for X, Y be RealNormSpace holds 0.
  R_VectorSpace_of_BoundedLinearOperators(X,Y) = (the carrier of X) --> 0.Y
proof
  let X, Y be RealNormSpace;
A1: 0.R_VectorSpace_of_LinearOperators(X,Y) =((the carrier of X) -->0.Y) by
Th18;
  R_VectorSpace_of_BoundedLinearOperators(X,Y) is Subspace of
  R_VectorSpace_of_LinearOperators(X,Y) by Th22,RSSPACE:11;
  hence thesis by A1,RLSUB_1:11;
end;
