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Rodolphe Lepigre
Iris
Commits
d392b7a6
Commit
d392b7a6
authored
Jul 05, 2019
by
Robbert Krebbers
Browse files
Add lemma `big_sepL2_reverse`.
parent
18d6dd40
Changes
1
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Inline
Side-by-side
theories/bi/big_op.v
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d392b7a6
...
...
@@ -400,6 +400,17 @@ Section sep_list2.
by
f_equiv
;
f_equiv
=>
k
[??].
Qed
.
Lemma
big_sepL2_reverse_2
(
Φ
:
A
→
B
→
PROP
)
l1
l2
:
([
∗
list
]
y1
;
y2
∈
l1
;
l2
,
Φ
y1
y2
)
⊢
([
∗
list
]
y1
;
y2
∈
reverse
l1
;
reverse
l2
,
Φ
y1
y2
).
Proof
.
revert
l2
.
induction
l1
as
[|
x1
l1
IH
]
;
intros
[|
x2
l2
]
;
simpl
;
auto
using
False_elim
.
rewrite
!
reverse_cons
(
comm
bi_sep
)
IH
.
by
rewrite
(
big_sepL2_app
_
_
[
x1
]
_
[
x2
])
big_sepL2_singleton
wand_elim_l
.
Qed
.
Lemma
big_sepL2_reverse
(
Φ
:
A
→
B
→
PROP
)
l1
l2
:
([
∗
list
]
y1
;
y2
∈
reverse
l1
;
reverse
l2
,
Φ
y1
y2
)
⊣
⊢
([
∗
list
]
y1
;
y2
∈
l1
;
l2
,
Φ
y1
y2
).
Proof
.
apply
(
anti_symm
_
)
;
by
rewrite
big_sepL2_reverse_2
?reverse_involutive
.
Qed
.
Lemma
big_sepL2_sep
Φ
Ψ
l1
l2
:
([
∗
list
]
k
↦
y1
;
y2
∈
l1
;
l2
,
Φ
k
y1
y2
∗
Ψ
k
y1
y2
)
⊣
⊢
([
∗
list
]
k
↦
y1
;
y2
∈
l1
;
l2
,
Φ
k
y1
y2
)
∗
([
∗
list
]
k
↦
y1
;
y2
∈
l1
;
l2
,
Ψ
k
y1
y2
).
...
...
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