
theorem Th14:
  for R being left_zeroed non empty addLoopStr, a being Element
  of R holds a * 1 = a
proof
  let R be left_zeroed non empty addLoopStr, a be Element of R;
  thus a * 1 = (Nat-mult-right(R)).(a,0+1)
    .= (Nat-mult-right(R)).(a,0) + a by Def4
    .= 0.R + a by Def4
    .= a by ALGSTR_1:def 2;
end;
