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Rodolphe Lepigre
Iris
Commits
6cb0f4d2
Commit
6cb0f4d2
authored
Nov 28, 2017
by
Robbert Krebbers
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Some lemmas about discreteness.
parent
fc9e25a5
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+5
-3
theories/algebra/cmra.v
theories/algebra/cmra.v
+4
-0
theories/algebra/ofe.v
theories/algebra/ofe.v
+1
-3
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theories/algebra/cmra.v
View file @
6cb0f4d2
...
...
@@ -555,11 +555,15 @@ Proof.
split
;
first
by
rewrite
cmra_valid_validN
.
eauto
using
cmra_discrete_valid
,
cmra_validN_le
with
lia
.
Qed
.
Lemma
cmra_discrete_valid_iff_0
`
{
CmraDiscrete
A
}
n
x
:
✓
{
0
}
x
↔
✓
{
n
}
x
.
Proof
.
by
rewrite
-!
cmra_discrete_valid_iff
.
Qed
.
Lemma
cmra_discrete_included_iff
`
{
OfeDiscrete
A
}
n
x
y
:
x
≼
y
↔
x
≼
{
n
}
y
.
Proof
.
split
;
first
by
apply
cmra_included_includedN
.
intros
[
z
->%(
discrete_iff
_
_
)]
;
eauto
using
cmra_included_l
.
Qed
.
Lemma
cmra_discrete_included_iff_0
`
{
OfeDiscrete
A
}
n
x
y
:
x
≼
{
0
}
y
↔
x
≼
{
n
}
y
.
Proof
.
by
rewrite
-!
cmra_discrete_included_iff
.
Qed
.
(** Cancelable elements *)
Global
Instance
cancelable_proper
:
Proper
(
equiv
==>
iff
)
(@
Cancelable
A
).
...
...
theories/algebra/ofe.v
View file @
6cb0f4d2
...
...
@@ -190,9 +190,7 @@ Section ofe.
split
;
intros
;
auto
.
apply
(
discrete
_
),
dist_le
with
n
;
auto
with
lia
.
Qed
.
Lemma
discrete_iff_0
n
(
x
:
A
)
`
{!
Discrete
x
}
y
:
x
≡
{
0
}
≡
y
↔
x
≡
{
n
}
≡
y
.
Proof
.
split
=>
?.
by
apply
equiv_dist
,
(
discrete
_
).
eauto
using
dist_le
with
lia
.
Qed
.
Proof
.
by
rewrite
-!
discrete_iff
.
Qed
.
End
ofe
.
(** Contractive functions *)
...
...
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