Also remove some superfluous map_ prefixes.

Also, slightly reorganize.

Improve names, simplify definition of dist.

Shorten proofs and name variables that we introduce.

Requires should always be at the top of a file, Imports can be inside
of submodules.

It is strange that a Require in a submodule is allowed and then triggers
an error when using the whole module. This may be a Coq bug.

They will use Iris is a library, in that paper's repo

...but it does not work. Hu?