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Jonas Kastberg
iris
Commits
1a4f9850
Commit
1a4f9850
authored
Nov 16, 2017
by
Robbert Krebbers
Browse files
Shorten proof.
parent
fd2acffe
Changes
1
Hide whitespace changes
Inline
Side-by-side
theories/base_logic/derived.v
View file @
1a4f9850
...
...
@@ -981,13 +981,9 @@ Proof. rewrite -(plainly_plainly P); apply plainly_intro'. Qed.
Lemma
plainly_alt
P
:
■
P
⊣
⊢
P
≡
True
.
Proof
.
apply
(
anti_symm
(
⊢
)).
-
rewrite
-
prop_ext
.
apply
plainly_intro'
.
rewrite
plainly_elim
.
apply
and_intro
;
apply
impl_intro_r
.
+
apply
True_intro
.
+
apply
and_elim_l
.
-
rewrite
-
prop_ext
.
apply
plainly_mono
,
and_intro
;
apply
impl_intro_r
;
auto
.
-
rewrite
internal_eq_sym
(
internal_eq_rewrite
_
_
(
λ
P
,
■
P
)%
I
).
eapply
impl_elim
;
first
reflexivity
.
rewrite
plainly_pure
.
apply
True_intro
.
by
rewrite
plainly_pure
True_impl
.
Qed
.
Lemma
bupd_plain
P
`
{!
Plain
P
}
:
(|==>
P
)
⊢
P
.
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...
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