Technically, this is called Guard Prevention, however, I like to call it "Flip Prevention".
So the idea is this:
You've Side Mounted on someone. They might bring their elbow/forearm down by your hip. In a super technical scenario, they bring their arm/elbow down on your hip to push and create a little space so they can shrimp and shoot, and put you into their guard. Chances are slim to NONE that this will happen in an actual street fight. It is a highly specialized and technical move, that is not at all very intuitive to an aggressive attacker on the street.
What is more likely is that after they try rolling you off, and they find that they can't, they might sneak their arm/elbow down there, and try to flip you off. It's very effective, because they have controlled your hip!
Have your partner do it to you, so you can feel that that flipping you over move is a very legitimate threat to your position.
Once you've done that, now let's do the technique. From your arm that is under their arm (underhook) and from your posted foot, use that as your base to push upward from. That will give you just enough lift to slide your back leg through, going ahead of your posted left leg. Keep your torso and head low.
That motion gets your hips out of the question, and neutralizes that flip completely. Once you have done that, and they've calmed down a little, bring that leg that your brought forward back, but on the knee by their hip. At the same time, bring your other knee under their armpit. From here, you are about to do the Mount Transition.
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