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;
reserve K for Abelian right_zeroed add-associative right_complementable non
  empty addLoopStr,
  R,R1,R2,R3 for Element of i-tuples_on the carrier of K;

theorem
  -(R1 - R2) = R2 - R1
proof
  thus -(R1 - R2) = -(R1 + -R2) by FINSEQOP:84
    .= -R1 + --R2 by Th31
    .= -R1 + R2 by Th28
    .= R2 + -R1 by FINSEQOP:33
    .= R2 - R1 by FINSEQOP:84;
end;
