
theorem Th10:
  for K be Abelian non empty addLoopStr for V be non empty
  ModuleStr over K for f,g be Functional of V holds f+g = g+f
proof
  let K be Abelian non empty addLoopStr;
  let V be non empty ModuleStr over K;
  let f,g be Functional of V;
  now
    let x be Element of V;
    thus (f+g).x = f.x + g.x by Def3
      .= (g+f).x by Def3;
  end;
  hence thesis by FUNCT_2:63;
end;
