1.) First `simpl` away all the functors 2.) Don't use `done`, which calls `split`.

Also rename the recently added `view_update_alloc_frac` into
`view_update_frac_alloc` to be consistent with other lemmas about the
placement of `_frac`.

Use infix `_frac` for the `●{q}` variants. This was already done for the
external validity lemmas, but not for those for inclusion and internal validity.