reserve V for non empty RealLinearSpace;
reserve S for Real_Sequence;
reserve k,n,m,m1 for Nat;
reserve g,h,r,x for Real;

theorem Th35:
  for X be RealNormSpace, f,g,h be Point of DualSp X
    holds h = f+g iff for x be VECTOR of X holds h.x = f.x + g.x
proof
  let X be RealNormSpace;
  let f,g,h be Point of DualSp X;
  reconsider f1=f, g1=g, h1=h as VECTOR of
  R_VectorSpace_of_BoundedLinearFunctionals X;
  h=f+g iff h1=f1+g1;
  hence thesis by Th24;
end;
