If experimentally it can be proven that the velocity of a falling magnet through a coil is proportional to the emf induced, has it also been proven that dB/dt is proportional to the emf induced and how so ?
For slowly moving magnets, you can measure the strength of the magnetic field using another magnet mounted on a torsion balance. The degree of deflection would be proportional to the field strength. For fast moving magnets, you run into difficulties with your apparatus "lagging behind" and it is more properly the case that we measure $dB/dt$ by measuring things like EMF. The reason we do this is because mechanics and electrodynamics seem to be self-consistent. In other words, we believe it to be the case because the theory makes the right predictions. The proof, as you would say, is in the pudding.