transitive butt jealousy

For any person A, the enviability of A's butt is a quantity which describes the desirable traits of A's butt. If A's butt is less enviable than B's butt for some other person B, we say that A is jealous of B's butt, denoted by A ⩋᷾ B.

Let p1, p2, p3 be people such that p1 ⩋᷾ p2 and p2 ⩋᷾ p3. We can show that p1 ⩋᷾ p3 by contradiction:

Assume that p1 ⩋᷾ p3 is false. This implies that p1's butt is at least equally enviable as p3's. However, p1's butt is known to be less enviable than p2's, and p2's butt is known to be less enviable than p3's, implying that p1's butt must be strictly less enviable than p3's - a contradiction. Therefore, we can see that p1 ⩋᷾ p3 must be true, and therefore that the ⩋᷾ relation must be transitive.

i have to go to bed so y'all won't get to see the Butt Jealousy-Enviability Lowering lemma, maybe i'll finish that up later