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Tej Chajed
iris
Commits
c65aad41
Commit
c65aad41
authored
Dec 05, 2016
by
Jacques-Henri Jourdan
Browse files
List big op is compatible with permutations.
parent
0dd40006
Changes
1
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Inline
Side-by-side
algebra/cmra_big_op.v
View file @
c65aad41
...
...
@@ -154,6 +154,13 @@ Section list.
(
∀
k
y
,
l
!!
k
=
Some
y
→
f
k
y
≡
g
k
y
)
→
([
⋅
list
]
k
↦
y
∈
l
,
f
k
y
)
≡
([
⋅
list
]
k
↦
y
∈
l
,
g
k
y
).
Proof
.
apply
big_opL_forall
;
apply
_
.
Qed
.
Lemma
big_opL_permutation
(
f
:
A
→
M
)
l1
l2
:
l1
≡
ₚ
l2
→
([
⋅
list
]
x
∈
l1
,
f
x
)
≡
([
⋅
list
]
x
∈
l2
,
f
x
).
Proof
.
assert
(
∀
l
,
imap
(
λ
_
x
,
f
x
)
l
=
map
f
l
)
as
EQ
;
last
by
rewrite
/
big_opL
!
EQ
=>->.
intros
l
;
revert
f
.
induction
l
as
[|??
IH
]=>//
f
.
rewrite
imap_cons
IH
//.
Qed
.
Global
Instance
big_opL_ne
l
n
:
Proper
(
pointwise_relation
_
(
pointwise_relation
_
(
dist
n
))
==>
(
dist
n
))
...
...
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