
theorem
  for R being add-associative left_zeroed right_zeroed
  right_complementable right-distributive non empty doubleLoopStr, I being
  right-ideal non empty Subset of R, a being Element of R holds a,a
  are_congruent_mod I
proof
  let R be add-associative left_zeroed right_zeroed right_complementable
  right-distributive non empty doubleLoopStr, I be right-ideal non empty
  Subset of R, a be Element of R;
  a - a = 0.R & 0.R in I by IDEAL_1:3,RLVECT_1:15;
  hence thesis;
end;
