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b7c27550
Commit
b7c27550
authored
May 30, 2016
by
Robbert Krebbers
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More consistent naming for CMRA/uPred duplication lemmas.
parent
ac1e918f
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11 additions
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7 deletions
+11
-7
algebra/cmra.v
algebra/cmra.v
+10
-6
algebra/upred.v
algebra/upred.v
+1
-1
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algebra/cmra.v
View file @
b7c27550
...
...
@@ -320,10 +320,10 @@ Lemma cmra_pcore_r' x cx : pcore x ≡ Some cx → x ⋅ cx ≡ x.
Proof
.
intros
(
cx'
&?&->)%
equiv_Some_inv_r'
.
by
apply
cmra_pcore_r
.
Qed
.
Lemma
cmra_pcore_idemp'
x
cx
:
pcore
x
≡
Some
cx
→
pcore
cx
≡
Some
cx
.
Proof
.
intros
(
cx'
&?&->)%
equiv_Some_inv_r'
.
eauto
using
cmra_pcore_idemp
.
Qed
.
Lemma
cmra_pcore_
pcore
x
cx
:
pcore
x
=
Some
cx
→
cx
⋅
cx
≡
cx
.
Proof
.
eauto
using
cmra_pcore_r'
,
cmra_pcore_idemp
.
Qed
.
Lemma
cmra_pcore_
pcore'
x
cx
:
pcore
x
≡
Some
cx
→
cx
⋅
cx
≡
cx
.
Proof
.
eauto
using
cmra_pcore_r'
,
cmra_pcore_idemp'
.
Qed
.
Lemma
cmra_pcore_
dup
x
cx
:
pcore
x
=
Some
cx
→
cx
≡
cx
⋅
cx
.
Proof
.
intros
;
symmetry
;
eauto
using
cmra_pcore_r'
,
cmra_pcore_idemp
.
Qed
.
Lemma
cmra_pcore_
dup'
x
cx
:
pcore
x
≡
Some
cx
→
cx
≡
cx
⋅
cx
.
Proof
.
intros
;
symmetry
;
eauto
using
cmra_pcore_r'
,
cmra_pcore_idemp'
.
Qed
.
Lemma
cmra_pcore_validN
n
x
cx
:
✓
{
n
}
x
→
pcore
x
=
Some
cx
→
✓
{
n
}
cx
.
Proof
.
intros
Hvx
Hx
%
cmra_pcore_l
.
move
:
Hvx
;
rewrite
-
Hx
.
apply
cmra_validN_op_l
.
...
...
@@ -333,6 +333,10 @@ Proof.
intros
Hv
Hx
%
cmra_pcore_l
.
move
:
Hv
;
rewrite
-
Hx
.
apply
cmra_valid_op_l
.
Qed
.
(** ** Persistent elements *)
Lemma
persistent_dup
x
`
{!
Persistent
x
}
:
x
≡
x
⋅
x
.
Proof
.
by
apply
cmra_pcore_dup'
with
x
.
Qed
.
(** ** Order *)
Lemma
cmra_included_includedN
n
x
y
:
x
≼
y
→
x
≼
{
n
}
y
.
Proof
.
intros
[
z
->].
by
exists
z
.
Qed
.
...
...
@@ -428,8 +432,8 @@ Section total_core.
Lemma
cmra_core_r
x
:
x
⋅
core
x
≡
x
.
Proof
.
by
rewrite
(
comm
_
x
)
cmra_core_l
.
Qed
.
Lemma
cmra_core_
core
x
:
core
x
⋅
core
x
≡
core
x
.
Proof
.
by
rewrite
-{
2
}(
cmra_core_idemp
x
)
cmra_core_r
.
Qed
.
Lemma
cmra_core_
dup
x
:
core
x
≡
core
x
⋅
core
x
.
Proof
.
by
rewrite
-{
3
}(
cmra_core_idemp
x
)
cmra_core_r
.
Qed
.
Lemma
cmra_core_validN
n
x
:
✓
{
n
}
x
→
✓
{
n
}
core
x
.
Proof
.
rewrite
-{
1
}(
cmra_core_l
x
)
;
apply
cmra_validN_op_l
.
Qed
.
Lemma
cmra_core_valid
x
:
✓
x
→
✓
core
x
.
...
...
algebra/upred.v
View file @
b7c27550
...
...
@@ -876,7 +876,7 @@ Proof. by unseal. Qed.
Lemma
always_and_sep_1
P
Q
:
□
(
P
∧
Q
)
⊢
□
(
P
★
Q
).
Proof
.
unseal
;
split
=>
n
x
?
[??].
exists
(
core
x
),
(
core
x
)
;
rewrite
cmra_core_core
;
auto
.
exists
(
core
x
),
(
core
x
)
;
rewrite
-
cmra_core_dup
;
auto
.
Qed
.
Lemma
always_and_sep_l_1
P
Q
:
(
□
P
∧
Q
)
⊢
(
□
P
★
Q
).
Proof
.
...
...
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