mining has nothing to do with checkpoints. they are a relict which is no longer needed excapt for fasten up an initial sync.
when bitcoin forks every miner who uses the new software is mining on the new chaing and every miner on the old one is mining the old chain.
so no assumption needed: its all mathematic nothing more
How will you know which blockchain to download if you don't know which of the 2 is the correct one?
the one which contains most work and follows the protocol specification of my client (changed blocksize would be another protocol)