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Pierre-Marie Pédrot
Iris
Commits
3663aaf3
Commit
3663aaf3
authored
Nov 20, 2016
by
Robbert Krebbers
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More big op lemmas.
parent
6d66d9d1
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2
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algebra/cmra_big_op.v
algebra/cmra_big_op.v
+3
-0
base_logic/big_op.v
base_logic/big_op.v
+3
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algebra/cmra_big_op.v
View file @
3663aaf3
...
...
@@ -267,6 +267,9 @@ Section gmap.
Lemma
big_opM_lookup
f
m
i
x
:
m
!!
i
=
Some
x
→
f
i
x
≼
[
⋅
map
]
k
↦
y
∈
m
,
f
k
y
.
Proof
.
intros
.
rewrite
big_opM_delete
//.
apply
cmra_included_l
.
Qed
.
Lemma
big_opM_lookup_dom
(
f
:
K
→
M
)
m
i
:
is_Some
(
m
!!
i
)
→
f
i
≼
[
⋅
map
]
k
↦
_
∈
m
,
f
k
.
Proof
.
intros
[
x
?].
by
eapply
(
big_opM_lookup
(
λ
i
x
,
f
i
)).
Qed
.
Lemma
big_opM_singleton
f
i
x
:
([
⋅
map
]
k
↦
y
∈
{[
i
:
=
x
]},
f
k
y
)
≡
f
i
x
.
Proof
.
...
...
base_logic/big_op.v
View file @
3663aaf3
...
...
@@ -330,6 +330,9 @@ Section gmap.
Lemma
big_sepM_lookup
Φ
m
i
x
:
m
!!
i
=
Some
x
→
([
∗
map
]
k
↦
y
∈
m
,
Φ
k
y
)
⊢
Φ
i
x
.
Proof
.
intros
.
apply
uPred_included
.
by
apply
:
big_opM_lookup
.
Qed
.
Lemma
big_sepM_lookup_dom
(
Φ
:
K
→
uPred
M
)
m
i
:
is_Some
(
m
!!
i
)
→
([
∗
map
]
k
↦
_
∈
m
,
Φ
k
)
⊢
Φ
i
.
Proof
.
intros
[
x
?].
by
eapply
(
big_sepM_lookup
(
λ
i
x
,
Φ
i
)).
Qed
.
Lemma
big_sepM_singleton
Φ
i
x
:
([
∗
map
]
k
↦
y
∈
{[
i
:
=
x
]},
Φ
k
y
)
⊣
⊢
Φ
i
x
.
Proof
.
by
rewrite
big_opM_singleton
.
Qed
.
...
...
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