theorem
  for K being Abelian right_zeroed add-associative right_complementable
  non empty addLoopStr, R,R1,R2 being Element of i-tuples_on the carrier of K
  holds R1 + R = R2 + R or R1 + R = R + R2 implies R1 = R2
proof
  let K be Abelian right_zeroed add-associative right_complementable non
  empty addLoopStr, R,R1,R2 be Element of i-tuples_on the carrier of K;
  R1 + R = R2 + R iff R1 + R = R + R2 by FINSEQOP:33;
  hence thesis by Lm4;
end;
