And I believe that when we talk about the gravitational pressure being larger than the outward pressure from the exclusion principle, it's a little more complicated. The exclusion principle cannot really be violated, no matter how high the pressure. However, if you increase the pressure enough, the typical energy of an electron becomes high enough that it can combine with a proton and form a neutron. That releases a neutrino (which is the primary source of neutrinos in a supernova).
Conserve energy. Commute with the Hamiltonian.