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According to the documentation
https://coq.inria.fr/distrib/current/refman/proof-engine/tactics.html#coq:cmd.create-hintdb,
when creating a hint database without discrimination, Coq uses the
legacy implementation, which only uses Discrimination Trees for goals
without evars and does not use opaqueness information. This commit
switches the hint databases of stdpp to the new implementation.

This was done using `sed --in-place 's/[[:space:]]\+$//' theories/*.v`.

For other operations, like `<$>`,  such lemmas appear to make little sense, since
they require premises involving `!!`.

This follows iris!387
This closes issue #54.

In accordance with
<!93>

The `Equiv` instance for the domain is not needed.

For example, change `(!! i)` into `(.!! x)` so that `!!` can also be used as
a prefix, as done in VST for example.

This closes issue #42.

I have used the `sed` script below. This script took care of nearly all uses
apart from a few occurrences where a space was missing, e.g. `(,foo)`. In
this case, `coqc` will just fail, allowing one to patch up things manually.

The script is slightly too eager on Iris developments, where it also replaces
`($ ...)` introduction patterns. When porting Iris developments you thus may
want to remove the line for `$`.

```
sed '
s/(= /(.= /g;
s/ =)/ =.)/g;
s/(≠ /(.≠ /g;
s/ ≠)/ ≠.)/g;
s/(≡ /(.≡ /g;
s/ ≡)/ ≡.)/g;
s/(≢ /(.≢ /g;
s/ ≢)/ ≢.)/g;
s/(∧ /(.∧ /g;
s/ ∧)/ ∧.)/g;
s/(∨ /(.∨ /g;
s/ ∨)/ ∨.)/g;
s/(↔ /(.↔ /g;
s/ ↔)/ ↔.)/g;
s/(→ /(.→ /g;
s/ →)/ →.)/g;
s/($ /(.$ /g;
s/(∘ /(.∘ /g;
s/ ∘)/ ∘.)/g;
s/(, /(., /g;
s/ ,)/ ,.)/g;
s/(∘ /(.∘ /g;
s/ ∘)/ ∘.)/g;
s/(∪ /(.∪ /g;
s/ ∪)/ ∪.)/g;
s/(⊎ /(.⊎ /g;
s/ ⊎)/ ⊎.)/g;
s/(∩ /(.∩ /g;
s/ ∩)/ ∩.)/g;
s/(∖ /(.∖ /g;
s/ ∖)/ ∖.)/g;
s/(⊆ /(.⊆ /g;
s/ ⊆)/ ⊆.)/g;
s/(⊈ /(.⊈ /g;
s/ ⊈)/ ⊈.)/g;
s/(⊂ /(.⊂ /g;
s/ ⊂)/ ⊂.)/g;
s/(⊄ /(.⊄ /g;
s/ ⊄)/ ⊄.)/g;
s/(∈ /(.∈ /g;
s/ ∈)/ ∈.)/g;
s/(∉ /(.∉ /g;
s/ ∉)/ ∉.)/g;
s/(≫= /(.≫= /g;
s/ ≫=)/ ≫=.)/g;
s/(!! /(.!! /g;
s/ !!)/ !!.)/g;
s/(⊑ /(.⊑ /g;
s/ ⊑)/ ⊑.)/g;
s/(⊓ /(.⊓ /g;
s/ ⊓)/ ⊓.)/g;
s/(⊔ /(.⊔ /g;
s/ ⊔)/ ⊔.)/g;
s/(:: /(.:: /g;
s/ ::)/ ::.)/g;
s/(++ /(.++ /g;
s/ ++)/ ++.)/g;
s/(≡ₚ /(.≡ₚ /g;
s/ ≡ₚ)/ ≡ₚ.)/g;
s/(≢ₚ /(.≢ₚ /g;
s/ ≢ₚ)/ ≢ₚ.)/g;
s/(::: /(.::: /g;
s/ :::)/ :::.)/g;
s/(+++ /(.+++ /g;
s/ +++)/ +++.)/g;
' -i $(find -name "*.v")
```

Get rid of using `Collection` and favor `set` everywhere. Also, prefer conversion
functions that are called `X_to_Y`.

The following sed script performs most of the renaming, with the exception of:

- `set`, which has been renamed into `propset`. I couldn't do this rename
  using `sed` since it's too context sensitive.
- There was a spurious rename of `Vec.of_list`, which I correctly manually.
- Updating some section names and comments.

```
sed '
s/SimpleCollection/SemiSet/g;
s/FinCollection/FinSet/g;
s/CollectionMonad/MonadSet/g;
s/Collection/Set\_/g;
s/collection\_simple/set\_semi\_set/g;
s/fin\_collection/fin\_set/g;
s/collection\_monad\_simple/monad\_set\_semi\_set/g;
s/collection\_equiv/set\_equiv/g;
s/\bbset/boolset/g;
s/mkBSet/BoolSet/g;
s/mkSet/PropSet/g;
s/set\_equivalence/set\_equiv\_equivalence/g;
s/collection\_subseteq/set\_subseteq/g;
s/collection\_disjoint/set\_disjoint/g;
s/collection\_fold/set\_fold/g;
s/collection\_map/set\_map/g;
s/collection\_size/set\_size/g;
s/collection\_filter/set\_filter/g;
s/collection\_guard/set\_guard/g;
s/collection\_choose/set\_choose/g;
s/collection\_ind/set\_ind/g;
s/collection\_wf/set\_wf/g;
s/map\_to\_collection/map\_to\_set/g;
s/map\_of\_collection/set\_to\_map/g;
s/map\_of\_list/list\_to\_map/g;
s/map\_of\_to_list/list\_to\_map\_to\_list/g;
s/map\_to\_of\_list/map\_to\_list\_to\_map/g;
s/\bof\_list/list\_to\_set/g;
s/\bof\_option/option\_to\_set/g;
s/elem\_of\_of\_list/elem\_of\_list\_to\_set/g;
s/elem\_of\_of\_option/elem\_of\_option\_to\_set/g;
s/collection\_not\_subset\_inv/set\_not\_subset\_inv/g;
s/seq\_set/set\_seq/g;
s/collections/sets/g;
s/collection/set/g;
' -i $(find -name "*.v")
```

Two reasons:

- The equality makes it very hard to use the lemma with `rewrite`.
- The version for lists `insert_zip_with` does not have the equality either.

Adding a hint without a database now triggers a deprecation warning in
Coq master (https://github.com/coq/coq/pull/8987).

- Interaction with delete
- Make name about map interacting with insert consistent.

This followed from discussions in https://gitlab.mpi-sws.org/FP/iris-coq/merge_requests/134

This follows the associativity in Haskell. So, something like

  f <$> g <$> h

Is now parsed as:

  (f <$> g) <$> h

Since the functor is a generalized form of function application, this also now
also corresponds with the associativity of function application, which is also
left associative.