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Jonas Kastberg
iris
Commits
625d60c3
Commit
625d60c3
authored
Oct 27, 2018
by
Robbert Krebbers
Browse files
Some useful BI derived lemmas.
parent
ea07fcbc
Changes
2
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Inline
Side-by-side
theories/bi/derived_laws_bi.v
View file @
625d60c3
...
...
@@ -385,6 +385,9 @@ Proof.
apply
wand_intro_l
.
rewrite
left_absorb
.
auto
.
Qed
.
Lemma
wand_trans
P
Q
R
:
(
P
-
∗
Q
)
∗
(
Q
-
∗
R
)
⊢
(
P
-
∗
R
).
Proof
.
apply
wand_intro_l
.
by
rewrite
assoc
!
wand_elim_r
.
Qed
.
Lemma
wand_curry
P
Q
R
:
(
P
-
∗
Q
-
∗
R
)
⊣
⊢
(
P
∗
Q
-
∗
R
).
Proof
.
apply
(
anti_symm
_
).
...
...
@@ -429,6 +432,9 @@ Lemma wand_entails P Q : (P -∗ Q)%I → P ⊢ Q.
Proof
.
intros
.
rewrite
-[
P
]
emp_sep
.
by
apply
wand_elim_l'
.
Qed
.
Lemma
entails_wand
P
Q
:
(
P
⊢
Q
)
→
(
P
-
∗
Q
)%
I
.
Proof
.
intros
->.
apply
wand_intro_r
.
by
rewrite
left_id
.
Qed
.
(* A version that works with rewrite, in which bi_emp_valid is unfolded. *)
Lemma
entails_wand'
P
Q
:
(
P
⊢
Q
)
→
emp
⊢
(
P
-
∗
Q
).
Proof
.
apply
entails_wand
.
Qed
.
Lemma
equiv_wand_iff
P
Q
:
(
P
⊣
⊢
Q
)
→
(
P
∗
-
∗
Q
)%
I
.
Proof
.
intros
->
;
apply
wand_iff_refl
.
Qed
.
...
...
theories/bi/plainly.v
View file @
625d60c3
...
...
@@ -188,6 +188,9 @@ Proof.
apply
plainly_mono
,
impl_elim
with
P
;
auto
.
Qed
.
Lemma
plainly_emp_2
:
emp
⊢
@{
PROP
}
■
emp
.
Proof
.
apply
plainly_emp_intro
.
Qed
.
Lemma
plainly_sep_dup
P
:
■
P
⊣
⊢
■
P
∗
■
P
.
Proof
.
apply
(
anti_symm
_
).
...
...
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