Anyone mind going over the math for why a stepped MC does not effect the preasure output by each cylinder?

A dual MC is set up with a floating piston between the two separate cylinders.

if we assume we are at steady state (piston no longer moving, just generating more or less force), that the brake line ports are plugged, and that this piston is not connected by a bar and the spring force is minimal when breaking, the pressure in the primary circuit (P1) is going to be the input force (Fin) divided by the plunger area (A1). Without any solid connection or added force between the two channels, Fin must be equal to the force the fluid in the first circuit applies to the floating piston (F1) must be equal to Fin. Secondly, the force the floating piston applies to the second circuit (F2) must be equal to the force applied by the fluid in the primary circuit. This force (F2) is equal to the pressure (P2) in the piston multiplied by the area applying the pressure (A2). Therefor, if the area of the two circuits are not identical, the pressure within them will be different as well