reserve X for non empty set;
reserve Y for RealLinearSpace;
reserve f,g,h for Element of Funcs(X,the carrier of Y);
reserve a,b for Real;
reserve u,v,w for VECTOR of RLSStruct(#Funcs(X,the carrier of Y), (FuncZero(X,
    Y)),FuncAdd(X,Y),FuncExtMult(X,Y)#);

theorem
  for X, Y be RealNormSpace holds RLSStruct (# BoundedLinearOperators(X,
Y), Zero_(BoundedLinearOperators(X,Y), R_VectorSpace_of_LinearOperators(X,Y)),
Add_(BoundedLinearOperators(X,Y), R_VectorSpace_of_LinearOperators(X,Y)), Mult_
    (BoundedLinearOperators(X,Y), R_VectorSpace_of_LinearOperators(X,Y)) #) is
  Subspace of R_VectorSpace_of_LinearOperators(X,Y) by Th22,RSSPACE:11;
