theorem BLTh14:
  for V, W being non empty ModuleStr over INT.Ring, f being Form of V,W,
  a being Element of INT.Ring, w be Vector of W
  holds FunctionalSAF(a*f,w) = a*FunctionalSAF(f,w)
  proof
    let V, W be non empty ModuleStr over INT.Ring, f be Form of V,W,
      a be Element of INT.Ring,
    w be Vector of W;
    now
      let v be Vector of V;
      thus (FunctionalSAF(a*f,w)).v = (a*f).(v,w) by BLTh9
      .= a*f.(v,w) by BLDef3
      .= a*(FunctionalSAF(f,w)).v by BLTh9
      .= (a*(FunctionalSAF(f,w))).v by HAHNBAN1:def 6;
    end;
    hence thesis by FUNCT_2:63;
  end;
