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3e1b5787
Commit
3e1b5787
authored
Feb 23, 2018
by
Robbert Krebbers
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Show that `plainly` is an internal version of validity.
parent
2c2f36f5
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theories/bi/derived_laws.v
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theories/bi/derived_laws.v
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3e1b5787
...
@@ 1083,6 +1083,13 @@ Qed.
...
@@ 1083,6 +1083,13 @@ Qed.
Lemma
impl_wand_plainly_2
P
Q
:
(
bi_plainly
P

∗
Q
)
⊢
(
bi_plainly
P
→
Q
).
Lemma
impl_wand_plainly_2
P
Q
:
(
bi_plainly
P

∗
Q
)
⊢
(
bi_plainly
P
→
Q
).
Proof
.
apply
impl_intro_l
.
by
rewrite
plainly_and_sep_l_1
wand_elim_r
.
Qed
.
Proof
.
apply
impl_intro_l
.
by
rewrite
plainly_and_sep_l_1
wand_elim_r
.
Qed
.
Lemma
valid_plainly
P
:
bi_valid
(
bi_plainly
P
)
↔
bi_valid
P
.
Proof
.
rewrite
/
bi_valid
.
split
;
intros
HP
.

by
rewrite
(
idemp
bi_and
emp
%
I
)
{
2
}
HP
plainly_and_emp_elim
.

by
rewrite
(
plainly_emp_intro
emp
%
I
)
HP
.
Qed
.
Section
plainly_affinely_bi
.
Section
plainly_affinely_bi
.
Context
`
{
BiAffine
PROP
}.
Context
`
{
BiAffine
PROP
}.
...
...
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