
theorem Th28:
  for K be right_zeroed non empty addLoopStr for V,W be non
  empty ModuleStr over K for v,u be Vector of V, w,t be Vector of W, f be
additiveSAF additiveFAF Form of V,W holds f.(v+u,w+t) = f.(v,w) + f.(v,t) + (f.
  (u,w) + f.(u,t))
proof
  let K be right_zeroed non empty addLoopStr;
  let V,W be non empty ModuleStr over K;
  let v,w be Vector of V, y,z be Vector of W, f be additiveSAF additiveFAF
  Form of V,W;
  set v1 = f.(v,y), v3 = f.(v,z), v4 = f.(w,y), v5 = f.(w,z);
  thus f.(v+w,y+z) = f.(v,y+z) + f.(w,y+z) by Th26
    .= (v1 + v3) + f.(w,y+z) by Th27
    .= v1 +v3 + (v4 + v5) by Th27;
end;
