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George Pirlea
Iris
Commits
92024176
Commit
92024176
authored
Dec 27, 2016
by
Robbert Krebbers
Browse files
Tweak entails_equiv_and.
parent
fb1712dd
Changes
1
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Inline
Side-by-side
theories/base_logic/derived.v
View file @
92024176
...
...
@@ -438,11 +438,7 @@ Global Instance False_sep : RightAbsorb (⊣⊢) False%I (@uPred_sep M).
Proof
.
intros
P
;
apply
(
anti_symm
_
)
;
auto
.
Qed
.
Lemma
entails_equiv_and
P
Q
:
(
P
⊣
⊢
Q
∧
P
)
↔
(
P
⊢
Q
).
Proof
.
split
;
first
by
intros
->
;
apply
uPred
.
and_elim_l
.
intros
PQ
.
apply
uPred
.
equiv_spec
;
split
;
[
by
apply
uPred
.
and_intro
|
apply
uPred
.
and_elim_r
].
Qed
.
Proof
.
split
.
by
intros
->
;
auto
.
intros
;
apply
(
anti_symm
_
)
;
auto
.
Qed
.
Lemma
sep_and_l
P
Q
R
:
P
∗
(
Q
∧
R
)
⊢
(
P
∗
Q
)
∧
(
P
∗
R
).
Proof
.
auto
.
Qed
.
Lemma
sep_and_r
P
Q
R
:
(
P
∧
Q
)
∗
R
⊢
(
P
∗
R
)
∧
(
Q
∗
R
).
...
...
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