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George Pirlea
Iris
Commits
31a0912c
Commit
31a0912c
authored
May 06, 2019
by
Robbert Krebbers
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Some additional results about `<affine>?p`.
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theories/bi/derived_laws_bi.v
theories/bi/derived_laws_bi.v
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theories/bi/derived_laws_bi.v
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31a0912c
...
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@@ -1144,6 +1144,13 @@ Proof. destruct p; simpl; auto using affinely_sep. Qed.
Lemma
affinely_if_idemp
p
P
:
<
affine
>
?p
<
affine
>
?p
P
⊣
⊢
<
affine
>
?p
P
.
Proof
.
destruct
p
;
simpl
;
auto
using
affinely_idemp
.
Qed
.
Lemma
affinely_if_and_l
p
P
Q
:
<
affine
>
?p
P
∧
Q
⊣
⊢
<
affine
>
?p
(
P
∧
Q
).
Proof
.
destruct
p
;
simpl
;
auto
using
affinely_and_l
.
Qed
.
Lemma
affinely_if_and_r
p
P
Q
:
P
∧
<
affine
>
?p
Q
⊣
⊢
<
affine
>
?p
(
P
∧
Q
).
Proof
.
destruct
p
;
simpl
;
auto
using
affinely_and_r
.
Qed
.
Lemma
affinely_if_and_lr
p
P
Q
:
<
affine
>
?p
P
∧
Q
⊣
⊢
P
∧
<
affine
>
?p
Q
.
Proof
.
destruct
p
;
simpl
;
auto
using
affinely_and_lr
.
Qed
.
(* Conditional absorbingly modality *)
Global
Instance
absorbingly_if_ne
p
:
NonExpansive
(@
bi_absorbingly_if
PROP
p
).
Proof
.
solve_proper
.
Qed
.
...
...
@@ -1468,10 +1475,14 @@ Global Instance persistently_persistent P : Persistent (<pers> P).
Proof
.
by
rewrite
/
Persistent
persistently_idemp
.
Qed
.
Global
Instance
affinely_persistent
P
:
Persistent
P
→
Persistent
(<
affine
>
P
).
Proof
.
rewrite
/
bi_affinely
.
apply
_
.
Qed
.
Global
Instance
affinely_if_persistent
p
P
:
Persistent
P
→
Persistent
(<
affine
>
?p
P
).
Proof
.
destruct
p
;
simpl
;
apply
_
.
Qed
.
Global
Instance
intuitionistically_persistent
P
:
Persistent
(
□
P
).
Proof
.
rewrite
/
bi_intuitionistically
.
apply
_
.
Qed
.
Global
Instance
absorbingly_persistent
P
:
Persistent
P
→
Persistent
(<
absorb
>
P
).
Proof
.
rewrite
/
bi_absorbingly
.
apply
_
.
Qed
.
Global
Instance
absorbingly_if_persistent
p
P
:
Persistent
P
→
Persistent
(<
absorb
>
?p
P
).
Proof
.
destruct
p
;
simpl
;
apply
_
.
Qed
.
Global
Instance
from_option_persistent
{
A
}
P
(
Ψ
:
A
→
PROP
)
(
mx
:
option
A
)
:
(
∀
x
,
Persistent
(
Ψ
x
))
→
Persistent
P
→
Persistent
(
from_option
Ψ
P
mx
).
Proof
.
destruct
mx
;
apply
_
.
Qed
.
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