
theorem Th13:
  for R being right_zeroed non empty addLoopStr, a being Element
  of R holds 1 * a = a
proof
  let R be right_zeroed non empty addLoopStr, a be Element of R;
  thus 1 * a = (Nat-mult-left(R)).(0+1,a)
    .= a + (Nat-mult-left(R)).(0,a) by Def3
    .= a + 0.R by Def3
    .= a by RLVECT_1:def 4;
end;
