
theorem HTh14:
  for V, W being non empty ModuleStr over INT.Ring, f being FrForm of V,W,
  a being Element of F_Real, w being Vector of W holds
  FrFunctionalSAF(a*f,w) = a*FrFunctionalSAF(f,w)
  proof
    let V, W be non empty ModuleStr over INT.Ring, f be FrForm of V,W,
    a be Element of F_Real, w be Vector of W;
    now
      let v be Vector of V;
      thus (FrFunctionalSAF(a*f,w)).v = (a*f).(v,w) by HTh9
      .= a*f.(v,w) by Def3
      .= a*(FrFunctionalSAF(f,w)).v by HTh9
      .= (a*(FrFunctionalSAF(f,w))).v by HDef6;
    end;
    hence thesis by FUNCT_2:63;
  end;
