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Jonas Kastberg
iris
Commits
b58adc74
Commit
b58adc74
authored
Oct 24, 2018
by
Robbert Krebbers
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Plain Diff
Prove `(|==> ∀ x, Φ x) ⊣⊢ (∀ x, |==> Φ x)` for plain `Φ`.
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44dc86c8
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theories/bi/updates.v
theories/bi/updates.v
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theories/bi/updates.v
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b58adc74
...
...
@@ -156,8 +156,21 @@ Section bupd_derived_sbi.
by
rewrite
-
bupd_intro
-
or_intro_l
.
Qed
.
Lemma
bupd_plain
P
`
{
BiBUpdPlainly
PROP
,
!
Plain
P
}
:
(|==>
P
)
⊢
P
.
Proof
.
by
rewrite
{
1
}(
plain
P
)
bupd_plainly
.
Qed
.
Section
bupd_plainly
.
Context
`
{
BiBUpdPlainly
PROP
}.
Lemma
bupd_plain
P
`
{!
Plain
P
}
:
(|==>
P
)
⊢
P
.
Proof
.
by
rewrite
{
1
}(
plain
P
)
bupd_plainly
.
Qed
.
Lemma
bupd_forall
{
A
}
(
Φ
:
A
→
PROP
)
`
{
∀
x
,
Plain
(
Φ
x
)}
:
(|==>
∀
x
,
Φ
x
)
⊣
⊢
(
∀
x
,
|==>
Φ
x
).
Proof
.
apply
(
anti_symm
_
).
-
apply
forall_intro
=>
x
.
by
rewrite
(
forall_elim
x
).
-
rewrite
-
bupd_intro
.
apply
forall_intro
=>
x
.
by
rewrite
(
forall_elim
x
)
bupd_plain
.
Qed
.
End
bupd_plainly
.
End
bupd_derived_sbi
.
Section
fupd_derived
.
...
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