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;

theorem
  -R1 = -R2 implies R1 = R2
proof
  assume -R1 = -R2;
  hence R1 = --R2 by Th28
    .= R2 by Th28;
end;
