
theorem Th13:
  for K be right_zeroed non empty addLoopStr for V be non empty
  ModuleStr over K for f be Functional of V holds f + 0Functional(V) = f
proof
  let K be right_zeroed non empty addLoopStr;
  let V be non empty ModuleStr over K;
  let f be Functional of V;
  now
    let x be Element of V;
    thus (f+0Functional(V)).x = f.x+(0Functional(V)).x by Def3
      .= f.x+0.K by FUNCOP_1:7
      .= f.x by RLVECT_1:def 4;
  end;
  hence thesis by FUNCT_2:63;
end;
