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f72ccbec
Commit
f72ccbec
authored
Jun 13, 2017
by
Robbert Krebbers
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Remove primitive rule `□ (P ∧ Q) ⊢ □ (P ∗ Q)`.
It can be derived, thanks to Ales for noticing!
parent
6d89cb87
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2
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10 additions
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9 deletions
+10
-9
theories/base_logic/derived.v
theories/base_logic/derived.v
+10
-4
theories/base_logic/primitive.v
theories/base_logic/primitive.v
+0
-5
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theories/base_logic/derived.v
View file @
f72ccbec
...
...
@@ -479,6 +479,8 @@ Proof. intros P Q; apply always_mono. Qed.
Lemma
always_intro'
P
Q
:
(
□
P
⊢
Q
)
→
□
P
⊢
□
Q
.
Proof
.
intros
<-.
apply
always_idemp
.
Qed
.
Lemma
always_idemp
P
:
□
□
P
⊣
⊢
□
P
.
Proof
.
apply
(
anti_symm
_
)
;
auto
using
always_idemp
.
Qed
.
Lemma
always_pure
φ
:
□
⌜φ⌝
⊣
⊢
⌜φ⌝
.
Proof
.
apply
(
anti_symm
_
)
;
auto
using
always_pure_2
.
Qed
.
...
...
@@ -509,16 +511,20 @@ Proof.
rewrite
-(
internal_eq_refl
a
)
always_pure
;
auto
.
Qed
.
Lemma
always_and_sep
P
Q
:
□
(
P
∧
Q
)
⊣
⊢
□
(
P
∗
Q
).
Proof
.
apply
(
anti_symm
(
⊢
))
;
auto
using
always_and_sep_1
.
Qed
.
Lemma
always_and_sep_l'
P
Q
:
□
P
∧
Q
⊣
⊢
□
P
∗
Q
.
Proof
.
apply
(
anti_symm
(
⊢
))
;
auto
using
always_and_sep_l_1
.
Qed
.
Lemma
always_and_sep_r'
P
Q
:
P
∧
□
Q
⊣
⊢
P
∗
□
Q
.
Proof
.
by
rewrite
!(
comm
_
P
)
always_and_sep_l'
.
Qed
.
Lemma
always_sep_dup'
P
:
□
P
⊣
⊢
□
P
∗
□
P
.
Proof
.
by
rewrite
-
always_and_sep_l'
idemp
.
Qed
.
Lemma
always_and_sep
P
Q
:
□
(
P
∧
Q
)
⊣
⊢
□
(
P
∗
Q
).
Proof
.
apply
(
anti_symm
(
⊢
))
;
auto
.
rewrite
-{
1
}
always_idemp
always_and
always_and_sep_l'
;
auto
.
Qed
.
Lemma
always_sep
P
Q
:
□
(
P
∗
Q
)
⊣
⊢
□
P
∗
□
Q
.
Proof
.
by
rewrite
-
always_and_sep
-
always_and_sep_l'
always_and
.
Qed
.
Lemma
always_sep_dup'
P
:
□
P
⊣
⊢
□
P
∗
□
P
.
Proof
.
by
rewrite
-
always_sep
-
always_and_sep
(
idemp
_
).
Qed
.
Lemma
always_wand
P
Q
:
□
(
P
-
∗
Q
)
⊢
□
P
-
∗
□
Q
.
Proof
.
by
apply
wand_intro_r
;
rewrite
-
always_sep
wand_elim_l
.
Qed
.
...
...
theories/base_logic/primitive.v
View file @
f72ccbec
...
...
@@ -437,11 +437,6 @@ Proof. by unseal. Qed.
Lemma
always_exist_1
{
A
}
(
Ψ
:
A
→
uPred
M
)
:
(
□
∃
a
,
Ψ
a
)
⊢
(
∃
a
,
□
Ψ
a
).
Proof
.
by
unseal
.
Qed
.
Lemma
always_and_sep_1
P
Q
:
□
(
P
∧
Q
)
⊢
□
(
P
∗
Q
).
Proof
.
unseal
;
split
=>
n
x
?
[??].
exists
(
core
x
),
(
core
x
)
;
rewrite
-
cmra_core_dup
;
auto
.
Qed
.
Lemma
always_and_sep_l_1
P
Q
:
□
P
∧
Q
⊢
□
P
∗
Q
.
Proof
.
unseal
;
split
=>
n
x
?
[??]
;
exists
(
core
x
),
x
;
simpl
in
*.
...
...
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