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 - R3 = R1 - (R2 + R3)
proof
  thus R1 - R2 - R3 = R1 - R2 + - R3 by FINSEQOP:84
    .= R1 + - R2 + - R3 by FINSEQOP:84
    .= R1 + (- R2 + - R3) by FINSEQOP:28
    .= R1 + -(R2 + R3) by Th31
    .= R1 - (R2 + R3) by FINSEQOP:84;
end;
