reserve i,j,k for Nat;

theorem Th6:
  for K being left_zeroed right_zeroed non empty addLoopStr holds
  0.K is_a_unity_wrt the addF of K
proof
  let K be left_zeroed right_zeroed non empty addLoopStr;
  now
    let a be Element of K;
    thus (the addF of K).(0.K,a) = 0.K + a .= a by ALGSTR_1:def 2;
    thus (the addF of K).(a,0.K) = a + 0.K .= a by RLVECT_1:def 4;
  end;
  hence thesis by BINOP_1:3;
end;
