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Rodolphe Lepigre
Iris
Commits
fdec4152
Commit
fdec4152
authored
Feb 11, 2016
by
Robbert Krebbers
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Missing cmra_preserving lemmas.
parent
ee3b01dd
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algebra/cmra.v
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algebra/cmra.v
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fdec4152
...
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@@ -272,8 +272,12 @@ Lemma cmra_unit_preserving x y : x ≼ y → unit x ≼ unit y.
Proof
.
rewrite
!
cmra_included_includedN
;
eauto
using
cmra_unit_preservingN
.
Qed
.
Lemma
cmra_included_unit
x
:
unit
x
≼
x
.
Proof
.
by
exists
x
;
rewrite
cmra_unit_l
.
Qed
.
Lemma
cmra_preservingN_l
n
x
y
z
:
x
≼
{
n
}
y
→
z
⋅
x
≼
{
n
}
z
⋅
y
.
Proof
.
by
intros
[
z1
Hz1
]
;
exists
z1
;
rewrite
Hz1
(
associative
op
).
Qed
.
Lemma
cmra_preserving_l
x
y
z
:
x
≼
y
→
z
⋅
x
≼
z
⋅
y
.
Proof
.
by
intros
[
z1
Hz1
]
;
exists
z1
;
rewrite
Hz1
(
associative
op
).
Qed
.
Lemma
cmra_preservingN_r
n
x
y
z
:
x
≼
{
n
}
y
→
x
⋅
z
≼
{
n
}
y
⋅
z
.
Proof
.
by
intros
;
rewrite
-!(
commutative
_
z
)
;
apply
cmra_preservingN_l
.
Qed
.
Lemma
cmra_preserving_r
x
y
z
:
x
≼
y
→
x
⋅
z
≼
y
⋅
z
.
Proof
.
by
intros
;
rewrite
-!(
commutative
_
z
)
;
apply
cmra_preserving_l
.
Qed
.
...
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