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Iris
Iris
Commits
135f1298
Commit
135f1298
authored
Feb 23, 2018
by
Robbert Krebbers
Browse files
Describe `plainly` in terms of equality.
parent
3e1b5787
Changes
1
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Inline
Side-by-side
theories/bi/derived_laws.v
View file @
135f1298
...
...
@@ -1916,7 +1916,17 @@ Proof.
rewrite
-(
internal_eq_refl
True
%
I
a
)
plainly_pure
;
auto
.
Qed
.
Lemma
plainly_alt
P
`
{!
Absorbing
P
}
:
bi_plainly
P
⊣
⊢
P
≡
True
.
Lemma
plainly_alt
P
:
bi_plainly
P
⊣
⊢
bi_affinely
P
≡
emp
.
Proof
.
rewrite
-
plainly_affinely
.
apply
(
anti_symm
(
⊢
)).
-
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
_
_
bi_plainly
).
by
rewrite
-
plainly_True_emp
plainly_pure
True_impl
.
Qed
.
Lemma
plainly_alt_absorbing
P
`
{!
Absorbing
P
}
:
bi_plainly
P
⊣
⊢
P
≡
True
.
Proof
.
apply
(
anti_symm
(
⊢
)).
-
rewrite
-
prop_ext
.
apply
plainly_mono
,
and_intro
;
apply
wand_intro_l
;
auto
.
...
...
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