theorem BLTh32:
  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 Form of V,W
  st f is homogeneousFAF
  holds f.(v,a*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 Form of V,W;
    set F = FunctionalFAF(f,v);
    assume f is homogeneousFAF;
    then
    A1: F is homogeneous;
    thus f.(v,r*y) = F.(r*y) by BLTh8
    .= r*F.y by A1
    .= r*f.(v,y) by BLTh8;
  end;
