reserve E,F,G for RealNormSpace;
reserve f for Function of E,F;
reserve g for Function of F,G;
reserve a,b,c for Point of E;
reserve t for Real;

theorem Th8:
  for f be Real_Sequence holds f (#) (NAT --> a) = f * a
  proof
    let f be Real_Sequence;
    let n be Element of NAT;
    thus (f (#) (NAT --> a)).n = f.n * (NAT --> a).n by NDIFF_1:def 2
    .= (f * a).n by NDIFF_1:def 3;
  end;
