
theorem
  for K be add-associative non empty addLoopStr for V,W be non empty
  ModuleStr over K for f,g,h be Form of V,W holds f+g+h = f+(g+h)
proof
  let K be add-associative non empty addLoopStr, V,W be non empty ModuleStr
  over K, f,g,h be Form of V,W;
  now
    let v be Vector of V, w be Vector of W;
    thus (f+g+h).(v,w) = (f+g).(v,w) + h.(v,w) by Def2
      .= f.(v,w) + g.(v,w)+ h.(v,w) by Def2
      .= f.(v,w) + (g.(v,w)+ h.(v,w)) by RLVECT_1:def 3
      .= f.(v,w) + (g+h).(v,w) by Def2
      .= (f+ (g+h)).(v,w) by Def2;
  end;
  hence thesis;
end;
