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 Th36:
  for X be RealNormSpace, f,h be Point of DualSp X, a be Real
    holds h = a*f iff for x be VECTOR of X holds h.x = a * f.x
proof
  let X be RealNormSpace;
  let f,h be Point of DualSp X;
  let a be Real;
  reconsider f1=f, h1=h
    as VECTOR of R_VectorSpace_of_BoundedLinearFunctionals X;
  h=a*f iff h1=a*f1;
  hence thesis by Th25;
end;
