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87abb52a
Commit
87abb52a
authored
Dec 09, 2016
by
Jacques-Henri Jourdan
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Lemmas about Big ops and contains.
parent
2407263c
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algebra/cmra_big_op.v
algebra/cmra_big_op.v
+3
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base_logic/big_op.v
base_logic/big_op.v
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algebra/cmra_big_op.v
View file @
87abb52a
...
...
@@ -157,6 +157,9 @@ Section list.
Lemma
big_opL_permutation
(
f
:
A
→
M
)
l1
l2
:
l1
≡
ₚ
l2
→
([
⋅
list
]
x
∈
l1
,
f
x
)
≡
([
⋅
list
]
x
∈
l2
,
f
x
).
Proof
.
intros
Hl
.
by
rewrite
/
big_opL
!
imap_const
Hl
.
Qed
.
Lemma
big_opL_contains
(
f
:
A
→
M
)
l1
l2
:
l1
`
contains
`
l2
→
([
⋅
list
]
x
∈
l1
,
f
x
)
≼
([
⋅
list
]
x
∈
l2
,
f
x
).
Proof
.
intros
Hl
.
apply
big_op_contains
.
rewrite
!
imap_const
.
by
rewrite
->
Hl
.
Qed
.
Global
Instance
big_opL_ne
l
n
:
Proper
(
pointwise_relation
_
(
pointwise_relation
_
(
dist
n
))
==>
(
dist
n
))
...
...
base_logic/big_op.v
View file @
87abb52a
...
...
@@ -219,6 +219,9 @@ Section list.
(
∀
k
y
,
l
!!
k
=
Some
y
→
Φ
k
y
⊣
⊢
Ψ
k
y
)
→
([
∗
list
]
k
↦
y
∈
l
,
Φ
k
y
)
⊣
⊢
([
∗
list
]
k
↦
y
∈
l
,
Ψ
k
y
).
Proof
.
apply
big_opL_proper
.
Qed
.
Lemma
big_sepL_contains
(
Φ
:
A
→
uPred
M
)
l1
l2
:
l1
`
contains
`
l2
→
([
∗
list
]
y
∈
l2
,
Φ
y
)
⊢
[
∗
list
]
y
∈
l1
,
Φ
y
.
Proof
.
intros
?.
apply
uPred_included
.
by
apply
:
big_opL_contains
.
Qed
.
Global
Instance
big_sepL_mono'
l
:
Proper
(
pointwise_relation
_
(
pointwise_relation
_
(
⊢
))
==>
(
⊢
))
...
...
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