Is it true that, for all positive $A$, $B$, $C$, $D$, if $A-B>C-D$ then $AD>BC$ ?
I'm just wondering about this, and I tested it with a bunch of integers and haven't found a counterexample yet. Is there a way to know if it's true?
If it is true, is it true for all positive reals, or just natural numbers?
(Here's how I'm asking myself in my head: "So you have two quantities, and each of them has two factors. A factor of the first quantity is larger than a factor of the second quantity by more than the amount by which the other factor of the first is smaller than that of the second. Is the first quantity always greater?")