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6b6381fe
Commit
6b6381fe
authored
Aug 05, 2016
by
Robbert Krebbers
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Use rvs in counter_example and integrate with adequacy to obtain False.
parent
bd660383
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program_logic/counter_examples.v
program_logic/counter_examples.v
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program_logic/counter_examples.v
View file @
6b6381fe
...
...
@@ -2,8 +2,7 @@ From iris.algebra Require Import upred.
From
iris
.
proofmode
Require
Import
tactics
.
(** This proves that we need the ▷ in a "Saved Proposition" construction with
name-dependend allocation. *)
(** We fork in [uPred M] for any M, but the proof would work in any BI. *)
name-dependend allocation. *)
Section
savedprop
.
Context
(
M
:
ucmraT
).
Notation
iProp
:
=
(
uPred
M
).
...
...
@@ -11,11 +10,10 @@ Section savedprop.
Implicit
Types
P
:
iProp
.
(* Saved Propositions and view shifts. *)
Context
(
sprop
:
Type
)
(
saved
:
sprop
→
iProp
→
iProp
)
(
pvs
:
iProp
→
iProp
).
Hypothesis
pvs_mono
:
∀
P
Q
,
(
P
⊢
Q
)
→
pvs
P
⊢
pvs
Q
.
Context
(
sprop
:
Type
)
(
saved
:
sprop
→
iProp
→
iProp
).
Hypothesis
sprop_persistent
:
∀
i
P
,
PersistentP
(
saved
i
P
).
Hypothesis
sprop_alloc_dep
:
∀
(
P
:
sprop
→
iProp
),
True
⊢
pvs
(
∃
i
,
saved
i
(
P
i
)).
∀
(
P
:
sprop
→
iProp
),
True
=
r
=>
(
∃
i
,
saved
i
(
P
i
)).
Hypothesis
sprop_agree
:
∀
i
P
Q
,
saved
i
P
∧
saved
i
Q
⊢
P
↔
Q
.
(* Self-contradicting assertions are inconsistent *)
...
...
@@ -44,14 +42,19 @@ Section savedprop.
Proof
.
iIntros
"#HQ !"
.
by
iApply
(
saved_is_A
i
(
¬
A
i
)).
Qed
.
(* We can obtain such a [Q i]. *)
Lemma
make_Q
:
True
⊢
pvs
(
∃
i
,
Q
i
)
.
Lemma
make_Q
:
True
=
r
=>
∃
i
,
Q
i
.
Proof
.
apply
sprop_alloc_dep
.
Qed
.
(* Put together all the pieces to derive a contradiction. *)
(* TODO: Have a lemma in upred.v that says that we cannot view shift to False. *)
Lemma
contradiction
:
True
⊢
pvs
False
.
Lemma
rvs_false
:
(
True
:
uPred
M
)
=
r
=>
False
.
Proof
.
rewrite
make_Q
.
apply
p
vs_mono
.
iDestruct
1
as
(
i
)
"HQ"
.
rewrite
make_Q
.
apply
uPred
.
r
vs_mono
.
iDestruct
1
as
(
i
)
"HQ"
.
iApply
(
no_self_contradiction
(
A
i
)).
by
iApply
Q_self_contradiction
.
Qed
.
Lemma
contradiction
:
False
.
Proof
.
apply
(@
uPred
.
adequacy
M
False
1
)
;
simpl
.
rewrite
-
uPred
.
later_intro
.
apply
rvs_false
.
Qed
.
End
savedprop
.
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