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Jonas Kastberg
iris
Commits
c148ac4d
Commit
c148ac4d
authored
Oct 26, 2018
by
Robbert Krebbers
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Prove `E2 ⊆ E1 → P ={E1,E2}=∗ P`.
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b33a29de
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theories/bi/updates.v
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theories/bi/updates.v
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c148ac4d
...
...
@@ -203,6 +203,13 @@ Section fupd_derived.
Lemma
fupd_wand_r
E1
E2
P
Q
:
(|={
E1
,
E2
}=>
P
)
∗
(
P
-
∗
Q
)
={
E1
,
E2
}=
∗
Q
.
Proof
.
by
rewrite
fupd_frame_r
wand_elim_r
.
Qed
.
Lemma
fupd_mask_weaken
E1
E2
P
`
{!
Absorbing
P
}
:
E2
⊆
E1
→
P
={
E1
,
E2
}=
∗
P
.
Proof
.
intros
?.
rewrite
-{
1
}(
right_id
emp
%
I
bi_sep
P
%
I
).
rewrite
(
fupd_intro_mask
E1
E2
emp
%
I
)
//.
by
rewrite
fupd_frame_l
sep_elim_l
.
Qed
.
Lemma
fupd_trans_frame
E1
E2
E3
P
Q
:
((
Q
={
E2
,
E3
}=
∗
emp
)
∗
|={
E1
,
E2
}=>
(
Q
∗
P
))
={
E1
,
E3
}=
∗
P
.
Proof
.
...
...
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