::::::Am sorry. I defined this in my proof. I stated that the product of any number by zero is zero. This is well-defined. You ought to reread the proof. It has been stated correctly. I did not need to prove that -1 * 0 = 0, nor did I have to prove that -0 = -1 * 0. Since both the LHS of each statement is the same, this is implies that 0 must be equal to -0. Transitivity of equality.