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Rodolphe Lepigre
Iris
Commits
fe62f378
Commit
fe62f378
authored
Aug 27, 2019
by
Michael Sammler
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added lemmas for list cmra
parent
666af42e
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theories/algebra/list.v
theories/algebra/list.v
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theories/algebra/list.v
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fe62f378
...
...
@@ -359,6 +359,9 @@ Section properties.
Global
Instance
list_singleton_core_id
i
(
x
:
A
)
:
CoreId
x
→
CoreId
{[
i
:
=
x
]}.
Proof
.
by
rewrite
!
core_id_total
list_core_singletonM
=>
->.
Qed
.
Lemma
list_singleton_snoc
l
x
:
{[
length
l
:
=
x
]}
⋅
l
≡
l
++
[
x
].
Proof
.
elim
:
l
=>
//=
??
<-.
by
rewrite
left_id
.
Qed
.
(* Update *)
Lemma
list_singleton_updateP
(
P
:
A
→
Prop
)
(
Q
:
list
A
→
Prop
)
x
:
...
...
@@ -446,6 +449,17 @@ Section properties.
x ~l~> y @ ml ≫= (!! i) → {[ i := x ]} ~l~> {[ i := y ]} @ ml.
Proof. intros; apply list_middle_local_update. by rewrite replicate_length. Qed.
*)
Lemma
list_alloc_singleton_local_update
x
l
:
✓
x
→
(
l
,
ε
)
~l
~>
(
l
++
[
x
],
{[
length
l
:
=
x
]}).
Proof
.
move
=>
?.
have
->
:
({[
length
l
:
=
x
]}
≡
{[
length
l
:
=
x
]}
⋅
ε
)
by
rewrite
right_id
.
rewrite
-
list_singleton_snoc
.
apply
op_local_update
=>
??.
rewrite
list_singleton_snoc
app_validN
cons_validN
.
split_and
?
=>
//
;
[|
constructor
].
by
apply
cmra_valid_validN
.
Qed
.
End
properties
.
(** Functor *)
...
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