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Iris
c
Commits
d6c74d53
Commit
d6c74d53
authored
Oct 02, 2018
by
Léon Gondelman
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proved substitution lemma
parent
9a8c087e
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theories/vcgen/vcgen.v
theories/vcgen/vcgen.v
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theories/vcgen/vcgen.v
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d6c74d53
...
...
@@ -352,13 +352,35 @@ Section vcg_spec.
Context
`
{
amonadG
Σ
}.
Arguments
subst
_
_
!
_
/.
Lemma
de_subst_subst_comm
E
x
de
dv
:
(
dexpr_interp
E
(
de_subst
E
x
dv
de
))
=
(
subst
x
(
dval_interp
E
dv
)
(
dexpr_interp
E
de
)).
Proof
.
induction
de
;
simplify_eq
/=
;
simpl_subst
;
try
(
repeat
match
goal
with
|
[
H
:
_
=
subst
_
_
_
|-
_
]
=>
rewrite
H
end
;
by
simpl_subst
)
;
by
destruct
(
decide
(
x
=
s
)).
Qed
.
Lemma
dce_subst_subst_comm
E
(
x
:
string
)
(
de
:
dcexpr
)
(
dv
:
dval
)
:
dcexpr_interp
E
(
dce_subst
E
x
dv
de
)
=
(
subst
x
(
dval_interp
E
dv
)
(
dcexpr_interp
E
de
))%
E
.
Proof
.
Admitted
.
induction
de
;
simplify_eq
/=
;
simpl_subst
;
try
(
repeat
match
goal
with
|
[
H
:
_
=
subst
_
_
_
|-
_
]
=>
rewrite
H
end
;
by
simpl_subst
).
-
by
rewrite
de_subst_subst_comm
.
-
destruct
(
decide
(
x
=
s
))
;
simplify_eq
/=
;
rewrite
IHde1
.
+
rewrite
decide_False
;
naive_solver
.
+
rewrite
IHde2
decide_True
;
naive_solver
.
Qed
.
Arguments
subst
:
simpl
never
.
Lemma
mapsto_wand_list_aux_spec
E
m
Φ
(
k
:
nat
)
:
Lemma
mapsto_wand_list_aux_spec
E
m
Φ
(
k
:
nat
)
:
mapsto_wand_list_aux
E
m
Φ
k
-
∗
([
∗
list
]
n
↦
dio
∈
m
,
from_option
(
λ
'
{|
denv_level
:
=
lv
;
denv_frac
:
=
q
;
denv_dval
:
=
dv
|},
...
...
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