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Paolo G. Giarrusso
iris
Commits
7991ed54
Commit
7991ed54
authored
1 year ago
by
Ralf Jung
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make fractional_split truly forwards lemmas
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512b208d
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iris/bi/lib/fractional.v
+13
-10
13 additions, 10 deletions
iris/bi/lib/fractional.v
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10 deletions
iris/bi/lib/fractional.v
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7991ed54
...
...
@@ -66,17 +66,20 @@ Section fractional.
Fractional
Φ
→
AsFractional
(
Φ
q
)
Φ
q
.
Proof
.
done
.
Qed
.
Lemma
fractional_split
P
P1
P2
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
P
⊣⊢
P1
∗
P2
.
Proof
.
by
move
=>
-
[
->
->
]
[
->
_]
[
->
_]
.
Qed
.
Lemma
fractional_split_1
P
P1
P2
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
P
-∗
P1
∗
P2
.
(** These lemmas are meant to be used when [P] is known but the split-up
pieces ([Φ], [q1], [q2]) are not.
See [fractional_merge] below for the dual situation. *)
Lemma
fractional_split
P
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
P
⊣⊢
Φ
q1
∗
Φ
q2
.
Proof
.
by
move
=>
-
[
->
->
]
.
Qed
.
Lemma
fractional_split_1
P
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
P
-∗
Φ
q1
∗
Φ
q2
.
Proof
.
intros
.
apply
bi
.
entails_wand
.
by
rewrite
-
(
fractional_split
P
)
.
Qed
.
Lemma
fractional_split_2
P
P1
P2
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
P
1
-∗
P
2
-∗
P
.
Lemma
fractional_split_2
P
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
Φ
q
1
-∗
Φ
q
2
-∗
P
.
Proof
.
intros
.
apply
bi
.
entails_wand
,
bi
.
wand_intro_r
.
by
rewrite
-
(
fractional_split
P
)
.
Qed
.
Lemma
fractional_merge
P1
P2
Φ
q1
q2
`{
!
Fractional
Φ
}
:
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