This seems to shorten type class search.

This required a new ectx axiom: Positivity of evaluation contexts. This axiom was
also present in the old Iris 1.1 development, back when it still derived lifting
axioms for ectx languages.

Also remove some superfluous map_ prefixes.

Also, slightly reorganize.

Improve names, simplify definition of dist.

Shorten proofs and name variables that we introduce.