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Pierre Roux
Iris
Commits
100690d5
Commit
100690d5
authored
4 years ago
by
Ralf Jung
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add gmap_view_alloc_big
parent
b008a6b2
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iris/algebra/lib/gmap_view.v
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25 additions, 1 deletion
iris/algebra/lib/gmap_view.v
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iris/algebra/lib/gmap_view.v
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100690d5
From
Coq
.
QArith
Require
Import
Qcanon
.
From
iris
.
algebra
Require
Export
view
gmap
dfrac
.
From
iris
.
algebra
Require
Import
local_updates
proofmode_classes
.
From
iris
.
algebra
Require
Import
local_updates
proofmode_classes
big_op
.
From
iris
.
prelude
Require
Import
options
.
(** * CMRA for a "view of a gmap".
...
...
@@ -323,6 +323,30 @@ Section lemmas.
rewrite
lookup_insert_ne
//.
Qed
.
Lemma
gmap_view_alloc_big
m
m'
dq
:
m'
##
ₘ
m
→
✓
dq
→
gmap_view_auth
1
m
~~>
gmap_view_auth
1
(
m'
∪
m
)
⋅
([
^
op
map
]
k
↦
v
∈
m'
,
gmap_view_frag
k
dq
v
)
.
Proof
.
revert
m
.
induction
m'
as
[|
k
v
m'
]
using
map_ind
.
{
intros
m
_
.
rewrite
big_opM_empty
left_id
right_id
.
done
.
}
intros
m
Hdisj
.
etrans
.
{
apply
IHm'
;
last
done
.
eapply
map_disjoint_weaken_l
;
first
done
.
apply
insert_subseteq
.
done
.
}
etrans
.
-
eapply
cmra_update_op
;
last
reflexivity
.
eapply
(
gmap_view_alloc
_
k
dq
);
last
done
.
apply
lookup_union_None
.
split
;
first
done
.
eapply
map_disjoint_Some_l
;
first
done
.
rewrite
lookup_insert
.
done
.
-
(* Turn goal into "L ≡ R". *)
eapply
cmra_update_proper
;
[
reflexivity
|
|
reflexivity
]
.
rewrite
-
assoc
.
f_equiv
.
+
rewrite
insert_union_l
.
done
.
+
rewrite
big_opM_insert
;
last
done
.
done
.
Qed
.
Lemma
gmap_view_delete
m
k
v
:
gmap_view_auth
1
m
⋅
gmap_view_frag
k
(
DfracOwn
1
)
v
~~>
gmap_view_auth
1
(
delete
k
m
)
.
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