reserve i,j,k for Nat;
reserve K for non empty addLoopStr,
  a for Element of K,
  p for FinSequence of the carrier of K,
  R for Element of i-tuples_on the carrier of K;
reserve K for left_zeroed right_zeroed add-associative right_complementable
  non empty addLoopStr,
  R,R1,R2 for Element of i-tuples_on the carrier of K;
reserve K for non empty addLoopStr,
  a1,a2 for Element of K,
  p1,p2 for FinSequence of the carrier of K,
  R1,R2 for Element of i-tuples_on the carrier of K;

theorem
  for K being left_zeroed right_zeroed add-associative
right_complementable non empty addLoopStr, R1,R2 being Element of i-tuples_on
  the carrier of K holds R1 - -R2 = R1 + R2
proof
  let K be left_zeroed right_zeroed add-associative right_complementable non
  empty addLoopStr, R1,R2 be Element of i-tuples_on the carrier of K;
  thus R1 - -R2 = R1 + --R2 by FINSEQOP:84
    .= R1 + R2 by Th28;
end;
