I thought I could derive an interesting Lemma from this. Turns out I cannot. But this one may still be useful, at some point.

This is shorter and more consistent with naming elsewhere.

This makes the proofs a lot nicer. I tried factoring out some properties
about finite maps, but this was not entirely satisfactory. It would be nice
to generalize from_heap_None and heap_singleton_inv_l somehow.

This works better with class interference.