Now all the small tests work, and the `swap` example passes as well.
The main idea for fixing `vcg_wp` for sequence,
is to change the continuation `(Φ : dval → wp_expr)` of `vcg_wp`
so that it takes `denv` as additional parameter.
Then, in `vcg_wp` all cases, except for the **sequence** and **store** are simply passing the continuation.
The `vcg_wp` for the sequence becomes :
```Coq
| dCSeq de1 de2 => vcg_wp E m de1 R (λ m' _, UMod (vcg_wp E (denv_unlock m') de2 R Φ))
```
The case for **store** is more subtle. The critical part is the case
where `vcg_sp E m de1 = Some (mIn, mOut, dv1)` and `dv1 = dLitV (dLitLoc (dLoc i))`,
where the continuation will make use of the function `denv_replace_full i dv2 m'` whose specification is
```Coq
Some m' = (denv_replace_full i dv m) →
∃ x q dv0 m0,
(denv_interp E m0 ∗ dloc_interp E (dLoc i) ↦(x , q ) dval_interp E dv0 ⊣⊢ denv_interp E m) ∧
(denv_interp E m0 ∗ dloc_interp E (dLoc i) ↦(LLvl, 1%Qp) dval_interp E dv ⊣⊢ denv_interp E m').
```
In that case, we do not need to generate `IsLoc dv1 ...`, inlining instead the precise form of
`dv1` in the resulting formula, using `denv_replace_full` in the end:
```Coq
| dCStore de1 de2 =>
match vcg_sp E m de1 with
| Some (mIn, mOut, dv1) =>
match dv1 with
| dLitV (dLitLoc (dLoc i)) =>
mapsto_star_list m
(mapsto_wand_list mIn
(vcg_wp E mIn de2 R (λ m' dv2,
mapsto_wand_list mOut
(MapstoStarFull (dLoc i) (λ _, (MapstoWand (dLoc i) dv2 LLvl 1%Qp
(match (denv_replace_full i dv2 m') with
| Some mf => (Φ mf dv2)
| None => Base False (*TODO: maybe this is too strong, return just (Φ m' dv2) *)
end)))))))
```
Note the comment for the case where `denv_replace_full i dv2 = None`.
Note also, that for the other cases, including `match vcg_sp E m de2 = Some (mIn, mOut, dv1)`,
the continuation is passed as such, without replacing its content.
For the latter case ( `match vcg_sp E m de2 = Some (mIn, mOut, dv1)`) we probably also need to
update the continuation as described above.
Finally, the correctness statement for the `vcg_wp` becomes :
```Coq
Lemma vcg_wp_correct R E m de Φ :
wp_interp E (vcg_wp E m de R Φ) ⊢
awp (dcexpr_interp E de) R
(λ v, ∃ dv m', ⌜dval_interp E dv = v⌝ ∧ wp_interp E (Φ m' dv)).
```
This statement is proven for all cases. Somehow surprisingly, the specification
for `denv_replace_full` was not needed. The reason for that is probably that the correctness
statement only affirms the bare existence of 'm'.