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9312ad02
Verified
Commit
9312ad02
authored
Aug 06, 2019
by
Paolo G. Giarrusso
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Clearer statement for propositional extensionality
- And use prop_ext instead of prop_ext_2 in other proofs.
parent
69971a15
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CHANGELOG.md
CHANGELOG.md
+2
-0
theories/bi/monpred.v
theories/bi/monpred.v
+1
-1
theories/bi/plainly.v
theories/bi/plainly.v
+12
-3
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CHANGELOG.md
View file @
9312ad02
...
...
@@ -159,6 +159,8 @@ Changes in Coq:
fractional camera (
`frac_auth`
) with unbounded fractions.
*
Changed
`frac_auth`
notation from
`●!`
/
`◯!`
to
`●F`
/
`◯F`
. sed script:
`s/◯!/◯F/g; s/●!/●F/g;`
.
*
Lemma
`prop_ext`
works in both directions; its default direction is the
opposite of what it used to be.
*
Rename
`C`
suffixes into
`O`
since we no longer use COFEs but OFEs. Also
rename
`ofe_fun`
into
`discrete_fun`
and the corresponding notation
`-c>`
into
`-d>`
. The renaming can be automatically done using the following script (on
...
...
theories/bi/monpred.v
View file @
9312ad02
...
...
@@ -923,7 +923,7 @@ Proof.
-
intros
P
.
split
=>
i
/=.
apply
bi
.
forall_intro
=>
_
.
by
apply
plainly_emp_intro
.
-
intros
P
Q
.
split
=>
i
.
apply
bi
.
sep_elim_l
,
_
.
-
intros
P
Q
.
split
=>
i
/=.
rewrite
(
monPred_equivI
P
Q
).
f_equiv
=>
j
.
by
rewrite
-
prop_ext_2
!(
bi
.
forall_elim
j
)
!
bi
.
pure_True
//
!
bi
.
True_impl
.
by
rewrite
prop_ext
!(
bi
.
forall_elim
j
)
!
bi
.
pure_True
//
!
bi
.
True_impl
.
-
intros
P
.
split
=>
i
/=.
rewrite
bi
.
later_forall
.
f_equiv
=>
j
.
by
rewrite
-
later_plainly_1
.
-
intros
P
.
split
=>
i
/=.
...
...
theories/bi/plainly.v
View file @
9312ad02
...
...
@@ -467,10 +467,19 @@ Proof.
rewrite
-(
internal_eq_refl
True
%
I
a
)
plainly_pure
;
auto
.
Qed
.
Lemma
prop_ext
P
Q
:
P
≡
Q
⊣
⊢
■
(
P
∗
-
∗
Q
).
Proof
.
apply
(
anti_symm
(
⊢
))
;
last
exact
:
prop_ext_2
.
apply
(
internal_eq_rewrite'
P
Q
(
λ
Q
,
■
(
P
∗
-
∗
Q
))%
I
)
;
[
solve_proper
|
done
|
].
rewrite
(
plainly_emp_intro
(
P
≡
Q
)%
I
).
apply
plainly_mono
,
wand_iff_refl
.
Qed
.
Lemma
plainly_alt
P
:
■
P
⊣
⊢
<
affine
>
P
≡
emp
.
Proof
.
rewrite
-
plainly_affinely_elim
.
apply
(
anti_symm
(
⊢
)).
-
rewrite
-
prop_ext_2
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
.
-
rewrite
prop_ext
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
.
+
by
rewrite
affinely_elim_emp
left_id
.
+
by
rewrite
left_id
.
-
rewrite
internal_eq_sym
(
internal_eq_rewrite
_
_
plainly
).
...
...
@@ -480,7 +489,7 @@ Qed.
Lemma
plainly_alt_absorbing
P
`
{!
Absorbing
P
}
:
■
P
⊣
⊢
P
≡
True
.
Proof
.
apply
(
anti_symm
(
⊢
)).
-
rewrite
-
prop_ext_2
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
;
auto
.
-
rewrite
prop_ext
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
;
auto
.
-
rewrite
internal_eq_sym
(
internal_eq_rewrite
_
_
plainly
).
by
rewrite
plainly_pure
True_impl
.
Qed
.
...
...
@@ -488,7 +497,7 @@ Qed.
Lemma
plainly_True_alt
P
:
■
(
True
-
∗
P
)
⊣
⊢
P
≡
True
.
Proof
.
apply
(
anti_symm
(
⊢
)).
-
rewrite
-
prop_ext_2
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
;
auto
.
-
rewrite
prop_ext
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
;
auto
.
by
rewrite
wand_elim_r
.
-
rewrite
internal_eq_sym
(
internal_eq_rewrite
_
_
(
λ
Q
,
■
(
True
-
∗
Q
))%
I
ltac
:
(
shelve
))
;
last
solve_proper
.
...
...
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