
theorem Th10:
  for X be non empty set for Y be RealNormSpace holds 0.
  R_VectorSpace_of_BoundedFunctions(X,Y) =(X -->0.Y)
proof
  let X be non empty set;
  let Y be RealNormSpace;
  R_VectorSpace_of_BoundedFunctions(X,Y) is Subspace of RealVectSpace(X,Y)
  & 0.RealVectSpace(X,Y) =(X -->0.Y) by Th6,LOPBAN_1:13,RSSPACE:11;
  hence thesis by RLSUB_1:11;
end;
