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d9c978e7
Commit
d9c978e7
authored
Feb 17, 2016
by
Ralf Jung
Browse files
some helpful lemmas relating pvs and wand
parent
90075bbf
Changes
1
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program_logic/pviewshifts.v
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d9c978e7
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@@ -146,6 +146,14 @@ Lemma pvs_impl_l E1 E2 P Q : (□ (P → Q) ∧ pvs E1 E2 P) ⊑ pvs E1 E2 Q.
Proof
.
by
rewrite
pvs_always_l
always_elim
impl_elim_l
.
Qed
.
Lemma
pvs_impl_r
E1
E2
P
Q
:
(
pvs
E1
E2
P
∧
□
(
P
→
Q
))
⊑
pvs
E1
E2
Q
.
Proof
.
by
rewrite
comm
pvs_impl_l
.
Qed
.
Lemma
pvs_wand_l
E1
E2
P
Q
R
:
P
⊑
pvs
E1
E2
Q
→
((
Q
-
★
R
)
★
P
)
⊑
pvs
E1
E2
R
.
Proof
.
intros
->
.
rewrite
pvs_frame_l
.
apply
pvs_mono
,
wand_elim_l
.
Qed
.
Lemma
pvs_wand_r
E1
E2
P
Q
R
:
P
⊑
pvs
E1
E2
Q
→
(
P
★
(
Q
-
★
R
))
⊑
pvs
E1
E2
R
.
Proof
.
rewrite
comm
.
apply
pvs_wand_l
.
Qed
.
Lemma
pvs_mask_frame
'
E1
E1
'
E2
E2
'
P
:
E1
'
⊆
E1
→
E2
'
⊆
E2
→
E1
∖
E1
'
=
E2
∖
E2
'
→
pvs
E1
'
E2
'
P
⊑
pvs
E1
E2
P
.
...
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