
theorem Th74:
  for R being left_zeroed right_add-cancelable right-distributive
non empty doubleLoopStr, I,J being right-ideal non empty Subset of R holds
  J c= I + J
proof
  let R be left_zeroed right_add-cancelable right-distributive non empty
  doubleLoopStr, I,J be right-ideal non empty Subset of R;
    let u be object;
    assume u in J;
    then reconsider u9 = u as Element of J;
    0.R is Element of I by Th3;
    then 0.R + u9 in {a + b where a,b is Element of R : a in I & b in J};
    hence u in I + J by ALGSTR_1:def 2;
end;
