Draft: add lemma lookup_insert_eq
For most map operations we have a lemma lookup_foo
that always applies -- except, ironically, for insert
.
Unfortunately the lemma really should be called lookup_insert
, but that name is already taken, so I called it lookup_insert_eq
. Arguably that would be a good name for the i = j
case and nicely symmetric with lookup_insert_ne
(well, the really symmetric version would take i = j
as precondition, which can make it easier to rewrite with). lookup_insert
is used a lot so I feel renaming might be a bit too disruptive...