Thanks to @tchajed for the initial version of this proof.

Here's one case this lemma might be useful. Suppose we want to
programmatically generate namespaces for e.g. locks:

```
Definition lockN (l : loc) := nroot .@ "lock" .@ l.
```

Then to know that two such namespaces are disjoint, we need to know
that the corresponding locations are distinct. For that we use
the lemma here introduced.

```
Lemma ne l1 l2 v1 v2 :
  l1 ↦ v1 -∗ l2 ↦ v2 -∗ ⌜l1 ≠ l2⌝.
Proof. iApply mapsto_mapsto_ne. (* goal ¬ ✓ 2%Qp *) by intros []. Qed.
```

Rename existing asymmetric lemma `singleton_included` into `singleton_included_l`.

`{o,r,ur}Functor_map_{ne,id,compose,contractive}`.

They follow the pattern of `wp_wand`.

This helps async proof checking (see
iris/iris!406 (comment 46759)).

Done with
```
gsed -i 's/seal \(.*\)\. by eexists. Qed./seal \1. Proof. by eexists. Qed./' \
  $(find theories/ -name '*.v')
```

And checked by inspecting the output of:
```
git grep '\bseal\b'|fgrep -v 'Proof. by eexists. Qed.'
```

Gregory Malecha authored 5 years ago and Robbert Krebbers committed 5 years ago

- remove "odd" comment
- move atomic triples to bi_scope