
theorem
  for L being right_zeroed non empty addLoopStr, a being Element of L
  holds 2 * a = a + a
  proof
    let L be right_zeroed non empty addLoopStr;
    let a be Element of L;
    (Nat-mult-left(L)).(0+1,a) = a + (Nat-mult-left(L)).(0,a) by BINOM:def 3
    .= a + 0.L by BINOM:def 3
    .= a by RLVECT_1:def 4;
    hence a+a = (Nat-mult-left(L)).(1+1,a) by BINOM:def 3
    .= 2*a;
  end;
