
theorem HTh27:
  for V,W being non empty ModuleStr over INT.Ring, v being Vector of V,
  u, w being Vector of W, f being FrForm of V,W st f is additiveFAF
  holds f.(v,u+w) = f.(v,u) + f.(v,w)
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let v be Vector of V, y,z be Vector of W, f be FrForm of V,W;
    set F = FrFunctionalFAF(f,v);
    assume f is additiveFAF;
    then
    A1: F is additive;
    thus f.(v,y+z) = F.(y+z) by HTh8
    .= F.y+F.z by A1
    .= f.(v,y) + F.z by HTh8
    .= f.(v,y) + f.(v,z) by HTh8;
  end;
