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1530f15f
Commit
1530f15f
authored
Jan 20, 2016
by
Robbert Krebbers
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More bigop properties.
parent
18841bdb
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modures/ra.v
View file @
1530f15f
...
...
@@ 125,6 +125,10 @@ Lemma ra_empty_least x : ∅ ≼ x.
Proof
.
by
exists
x
;
rewrite
(
left_id
_
_
).
Qed
.
(** * Big ops *)
Lemma
big_op_nil
:
big_op
(@
nil
A
)
=
∅
.
Proof
.
done
.
Qed
.
Lemma
big_op_cons
x
xs
:
big_op
(
x
::
xs
)
=
x
⋅
big_op
xs
.
Proof
.
done
.
Qed
.
Global
Instance
big_op_permutation
:
Proper
((
≡
ₚ
)
==>
(
≡
))
big_op
.
Proof
.
induction
1
as
[
x
xs1
xs2
?
IH

x
y
xs

xs1
xs2
xs3
]
;
simpl
;
auto
.
...
...
@@ 147,6 +151,9 @@ Proof.
*
by
transitivity
(
big_op
ys
)
;
[
apply
ra_included_r
].
*
by
transitivity
(
big_op
ys
).
Qed
.
Lemma
big_op_delete
xs
i
x
:
xs
!!
i
=
Some
x
→
x
⋅
big_op
(
delete
i
xs
)
≡
big_op
xs
.
Proof
.
by
intros
;
rewrite
{
2
}(
delete_Permutation
xs
i
x
).
Qed
.
Context
`
{
FinMap
K
M
}.
Lemma
big_opM_empty
:
big_opM
(
∅
:
M
A
)
≡
∅
.
...
...
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