
theorem HTh31:
  for V, W being non empty ModuleStr over INT.Ring, v being Vector of V,
  w being Vector of W, a being Element of INT.Ring, f being FrForm of V,W
  st f is homogeneousSAF holds f.(a*v,w) = a*f.(v,w)
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let v be Vector of V, y be Vector of W,
    r be Element of INT.Ring, f be FrForm of V,W;
    set F = FrFunctionalSAF(f,y);
    assume f is homogeneousSAF;
    then
    A1: F is homogeneous;
    thus f.(r*v,y) = F.(r*v) by HTh9
    .= r*F.v by A1
    .= r*f.(v,y) by HTh9;
  end;
