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ef6de2f9
Commit
ef6de2f9
authored
Dec 23, 2016
by
Jacques-Henri Jourdan
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New derived lemma : entails_equiv_and.
parent
dcab926c
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#3502
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in 10 minutes and 38 seconds
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theories/base_logic/derived.v
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theories/base_logic/derived.v
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ef6de2f9
...
...
@@ -437,6 +437,12 @@ Proof. intros P; apply (anti_symm _); auto. Qed.
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
.
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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