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Iris
Iris
Commits
249edc6c
Commit
249edc6c
authored
Dec 03, 2017
by
Robbert Krebbers
Browse files
More properties about the relation between wand and impl.
parent
3f768dd2
Changes
1
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Inline
Side-by-side
theories/bi/derived.v
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249edc6c
...
...
@@ -1339,6 +1339,13 @@ Proof.
by
rewrite
-
persistently_and_affinely_sep_l
affinely_and_r
affinely_and
idemp
.
Qed
.
Lemma
wand_impl_affinely_persistently
P
Q
:
(
□
P
-
∗
Q
)
⊣
⊢
(
bi_persistently
P
→
Q
).
Proof
.
apply
(
anti_symm
(
⊢
)).
-
apply
impl_intro_l
.
by
rewrite
persistently_and_affinely_sep_l
wand_elim_r
.
-
apply
wand_intro_l
.
by
rewrite
-
persistently_and_affinely_sep_l
impl_elim_r
.
Qed
.
(* The combined affinely plainly modality *)
Lemma
affinely_plainly_elim
P
:
■
P
⊢
P
.
Proof
.
apply
plainly_and_emp_elim
.
Qed
.
...
...
@@ -1377,6 +1384,9 @@ Proof.
by
rewrite
-
plainly_and_affinely_sep_l
affinely_and_r
affinely_and
idemp
.
Qed
.
Lemma
wand_impl_affinely_plainly
P
Q
:
(
■
P
-
∗
Q
)
⊣
⊢
(
bi_plainly
P
→
Q
).
Proof
.
by
rewrite
-(
persistently_plainly
P
)
wand_impl_affinely_persistently
.
Qed
.
(* Conditional affinely modality *)
Global
Instance
affinely_if_ne
p
:
NonExpansive
(@
bi_affinely_if
PROP
p
).
Proof
.
solve_proper
.
Qed
.
...
...
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