
theorem HTh26:
  for V, W being non empty ModuleStr over INT.Ring, v, u being Vector of V,
  w being Vector of W, f being FrForm of V,W st f is additiveSAF
  holds f.(v+u,w) = f.(v,w) + f.(u,w)
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let v, w be Vector of V, y be Vector of W, f be FrForm of V,W;
    set F=FrFunctionalSAF(f,y);
    assume f is additiveSAF;
    then
    A1: F is additive;
    thus f.(v+w,y) = F.(v+w) by HTh9
    .= F.v+F.w by A1
    .= f.(v,y) + F.w by HTh9
    .= f.(v,y) + f.(w,y) by HTh9;
  end;
