if a doesn't equal 0 then 1/a doesn't equal 0
if a doesn't equal 0 then (-1)/a = 1/(-a)
1. Since a + (-a) = 0, then we subtract (-a) on both sides and get
a = 0 - (-a).
So we get -(-a) = a
2. Since -(a) = (-a), then we use the result in 1 and get
-(a) * -(b) = (-a) * -(b) = -(-a) * b = a * b
This provides examples of proving several properties of real numbers.