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Pierre Roux
Iris
Commits
8e7e3982
Commit
8e7e3982
authored
5 years ago
by
Ralf Jung
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theories/base_logic/lib/own.v
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theories/base_logic/lib/own.v
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3 deletions
theories/base_logic/lib/own.v
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8e7e3982
...
...
@@ -148,7 +148,7 @@ Qed.
assertion. However, the map_updateP_alloc does not suffice to show this. *)
Lemma
own_alloc_strong_dep
(
f
:
gname
→
A
)
(
P
:
gname
→
Prop
)
:
pred_infinite
P
→
(
forall
γ
,
✓
(
f
γ
))
→
(
∀
γ
,
✓
(
f
γ
))
→
(|
==>
∃
γ
,
⌜
P
γ
⌝
∧
own
γ
(
f
γ
))
%
I
.
Proof
.
intros
HP
Ha
.
...
...
@@ -168,7 +168,7 @@ Proof.
intros
HP
Ha
.
eapply
own_alloc_strong_dep
with
(
f
:=
λ
_,
a
);
eauto
.
Qed
.
Lemma
own_alloc_cofinite_dep
(
f
:
gname
→
A
)
(
G
:
gset
gname
)
:
(
forall
γ
,
✓
(
f
γ
))
→
(|
==>
∃
γ
,
⌜
γ
∉
G
⌝
∧
own
γ
(
f
γ
))
%
I
.
(
∀
γ
,
✓
(
f
γ
))
→
(|
==>
∃
γ
,
⌜
γ
∉
G
⌝
∧
own
γ
(
f
γ
))
%
I
.
Proof
.
intros
Ha
.
apply
(
own_alloc_strong_dep
f
(
λ
γ
,
γ
∉
G
))=>
//.
...
...
@@ -182,7 +182,7 @@ Proof.
intros
Ha
.
eapply
own_alloc_cofinite_dep
with
(
f
:=
λ
_,
a
);
eauto
.
Qed
.
Lemma
own_alloc_dep
(
f
:
gname
→
A
)
:
(
forall
γ
,
✓
(
f
γ
))
→
(|
==>
∃
γ
,
own
γ
(
f
γ
))
%
I
.
(
∀
γ
,
✓
(
f
γ
))
→
(|
==>
∃
γ
,
own
γ
(
f
γ
))
%
I
.
Proof
.
intros
Ha
.
rewrite
/
uPred_valid
/
bi_emp_valid
(
own_alloc_cofinite_dep
f
∅
)
//
;
[]
.
apply
bupd_mono
,
exist_mono
=>?
.
eauto
using
and_elim_r
.
...
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