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Rodolphe Lepigre
Iris
Commits
d7ee81fd
Commit
d7ee81fd
authored
Dec 06, 2016
by
Robbert Krebbers
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Factor out some common properties about lists.
parent
7fe0d259
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3
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15 additions
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14 deletions
+15
-14
algebra/cmra_big_op.v
algebra/cmra_big_op.v
+1
-5
base_logic/big_op.v
base_logic/big_op.v
+3
-9
prelude/list.v
prelude/list.v
+11
-0
No files found.
algebra/cmra_big_op.v
View file @
d7ee81fd
...
...
@@ -156,11 +156,7 @@ Section list.
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
.
Proof
.
intros
Hl
.
by
rewrite
/
big_opL
!
imap_const
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 @
d7ee81fd
...
...
@@ -137,11 +137,7 @@ Proof. intros. apply uPred_included. by apply: big_op_contains. Qed.
Lemma
big_sep_elem_of
Ps
P
:
P
∈
Ps
→
[
∗
]
Ps
⊢
P
.
Proof
.
intros
.
apply
uPred_included
.
by
apply
:
big_sep_elem_of
.
Qed
.
Lemma
big_sep_elem_of_acc
Ps
P
:
P
∈
Ps
→
[
∗
]
Ps
⊢
P
∗
(
P
-
∗
[
∗
]
Ps
).
Proof
.
intros
(
Ps1
&
Ps2
&->)%
elem_of_list_split
.
rewrite
!
big_sep_app
/=.
rewrite
assoc
(
comm
_
_
P
)
-
assoc
.
by
apply
sep_mono_r
,
wand_intro_l
.
Qed
.
Proof
.
intros
[
k
->]%
elem_of_Permutation
.
by
apply
sep_mono_r
,
wand_intro_l
.
Qed
.
(** ** Persistence *)
Global
Instance
big_sep_persistent
Ps
:
PersistentL
Ps
→
PersistentP
([
∗
]
Ps
).
...
...
@@ -233,10 +229,8 @@ Section list.
l
!!
i
=
Some
x
→
([
∗
list
]
k
↦
y
∈
l
,
Φ
k
y
)
⊢
Φ
i
x
∗
(
Φ
i
x
-
∗
([
∗
list
]
k
↦
y
∈
l
,
Φ
k
y
)).
Proof
.
intros
Hli
.
apply
big_sep_elem_of_acc
.
revert
Φ
l
Hli
.
induction
i
as
[|?
IH
]=>
Φ
[]
//=
y
l
;
rewrite
imap_cons
.
-
intros
[=->].
constructor
.
-
intros
?.
constructor
.
by
apply
(
IH
(
_
∘
S
)).
intros
Hli
.
apply
big_sep_elem_of_acc
,
(
elem_of_list_lookup_2
_
i
).
by
rewrite
list_lookup_imap
Hli
.
Qed
.
Lemma
big_sepL_lookup
Φ
l
i
x
:
...
...
prelude/list.v
View file @
d7ee81fd
...
...
@@ -1292,6 +1292,15 @@ Lemma imap_fmap {B C} (f : nat → B → C) (g : A → B) l :
imap f (g <$> l) = imap (λ n, f n ∘ g) l.
Proof. unfold imap. generalize 0. induction l; csimpl; auto with f_equal. Qed.
Lemma imap_const {B} (f : A → B) l : imap (const f) l = f <$> l.
Proof. unfold imap. generalize 0. induction l; csimpl; auto with f_equal. Qed.
Lemma list_lookup_imap {B} (f : nat → A → B) l i : imap f l !! i = f i <$> l !! i.
Proof.
revert f i. induction l as [|x l IH]; intros f [|i]; try done.
rewrite imap_cons; simpl. by rewrite IH.
Qed.
(** ** Properties of the [mask] function *)
Lemma mask_nil f βs : mask f βs (@nil A) = [].
Proof. by destruct βs. Qed.
...
...
@@ -1401,6 +1410,8 @@ Proof.
revert i; induction l as [|y l IH]; intros [|i] ?; simplify_eq/=; auto.
by rewrite Permutation_swap, <-(IH i).
Qed.
Lemma elem_of_Permutation l x : x ∈ l → ∃ k, l ≡ₚ x :: k.
Proof. intros [i ?]%elem_of_list_lookup. eauto using delete_Permutation. Qed.
(** ** Properties of the [prefix_of] and [suffix_of] predicates *)
Global Instance: PreOrder (@prefix_of A).
...
...
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