
theorem Th2:
  for R being left_zeroed right_add-cancelable right-distributive
  non empty doubleLoopStr, a being Element of R holds a * 0.R = 0.R
proof
  let R be left_zeroed right_add-cancelable right-distributive non empty
  doubleLoopStr, a be Element of R;
  a * 0.R = a * (0.R + 0.R) by ALGSTR_1:def 2
    .= a * 0.R + a * 0.R by VECTSP_1:def 2;
  then a * 0.R + a * 0.R = 0.R + a * 0.R by ALGSTR_1:def 2;
  hence thesis by ALGSTR_0:def 4;
end;
