This reverts commit 327acdbd. I thought we could
get something with a contractive "un-injection" funtion, but that turns out to
be impossible.

This reverts commit 3cc38ff6.

The reverted pure hypotheses and variables appear in the wrong order.

Also remove some superfluous map_ prefixes.

Also, slightly reorganize.

Improve names, simplify definition of dist.

Should be restored later.

The only drawback is that we have to restrict iprod to finite types,
but that is fine.