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Rodolphe Lepigre
Iris
Commits
a953a68d
Commit
a953a68d
authored
Dec 13, 2016
by
Ralf Jung
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agree: prove non-step-indexed uninjection
parent
766dbcd2
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theories/algebra/agree.v
theories/algebra/agree.v
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theories/algebra/agree.v
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a953a68d
...
@@ -354,7 +354,7 @@ Proof.
...
@@ -354,7 +354,7 @@ Proof.
intros
a
b
?.
apply
equiv_dist
=>
n
.
apply
to_agree_injN
.
by
apply
equiv_dist
.
intros
a
b
?.
apply
equiv_dist
=>
n
.
apply
to_agree_injN
.
by
apply
equiv_dist
.
Qed
.
Qed
.
Lemma
to_agree_uninj
n
(
x
:
agree
A
)
:
✓
{
n
}
x
→
∃
y
:
A
,
to_agree
y
≡
{
n
}
≡
x
.
Lemma
to_agree_uninj
N
n
(
x
:
agree
A
)
:
✓
{
n
}
x
→
∃
y
:
A
,
to_agree
y
≡
{
n
}
≡
x
.
Proof
.
Proof
.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=.
split
.
split
.
...
@@ -362,6 +362,16 @@ Proof.
...
@@ -362,6 +362,16 @@ Proof.
-
apply
(
list_agrees_iff_setincl
_
)
;
first
set_solver
+.
done
.
-
apply
(
list_agrees_iff_setincl
_
)
;
first
set_solver
+.
done
.
Qed
.
Qed
.
Lemma
to_agree_uninj
(
x
:
agree
A
)
:
✓
x
→
∃
y
:
A
,
to_agree
y
≡
x
.
Proof
.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=.
split
.
-
apply
:
list_setincl_singleton_in
.
set_solver
+.
-
apply
(
list_agrees_iff_setincl
_
)
;
first
set_solver
+.
eapply
list_agrees_subrel
;
last
exact
:
Hl
;
[
apply
_
..|].
intros
???.
by
apply
equiv_dist
.
Qed
.
Lemma
to_agree_included
(
a
b
:
A
)
:
to_agree
a
≼
to_agree
b
↔
a
≡
b
.
Lemma
to_agree_included
(
a
b
:
A
)
:
to_agree
a
≼
to_agree
b
↔
a
≡
b
.
Proof
.
Proof
.
split
.
split
.
...
...
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