Hacker's Delight Theorem D4
The (informal) proof of Hacker’s Delight Theorem D4:
The largest possible fractional part resulting from the division is 
. In order for the output value of the floor function to change, you need to roll over to the next highest integer (even in the negative numbers — remember that we’re strictly adding a positive x); therefore, you need at least a positive delta of 
to achieve this, which is impossible, because it contradicts the upper bounds on x we set forth initially.
