
theorem Th11:
  for K be add-associative non empty addLoopStr for V be non
  empty ModuleStr over K for f,g,h be Functional of V holds f+g+h = f+(g+h)
proof
  let K be add-associative non empty addLoopStr;
  let V be non empty ModuleStr over K;
  let f,g,h be Functional of V;
  now
    let x be Element of V;
    thus (f+g+h).x = (f+g).x + h.x by Def3
      .= f.x + g.x + h.x by Def3
      .= f.x + (g.x + h.x) by RLVECT_1:def 3
      .= f.x + ((g+h).x) by Def3
      .= (f+(g+h)).x by Def3;
  end;
  hence thesis by FUNCT_2:63;
end;
