(related to Proposition: \(-(x+y)=-x-y\))
- From the existence of the negative numbers it follows that \[(x+y)+(-(x+y))=0.\]
- Adding \((-x)\) to both sides of the equation results in \[y+(-(x+y))=-x.\]
- On the other hand, from the unique solvability of the equation \(a+x=b\) with the solution \(x=b-a\) it follows that the equation \(y+z=-x\) has the unique solution \(z=-x-y\).
- This proofs the statement \(-(x+y)=-x-y\).
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983