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Rodolphe Lepigre
Iris
Commits
669217fe
Commit
669217fe
authored
Dec 14, 2016
by
Robbert Krebbers
Browse files
Simplify proofs relating nth to lookup.
Also make names more consistent.
parent
b1fa82f0
Changes
1
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Inline
Side-by-side
theories/prelude/list.v
View file @
669217fe
...
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@@ -477,24 +477,13 @@ Lemma list_lookup_middle l1 l2 x n :
n
=
length
l1
→
(
l1
++
x
::
l2
)
!!
n
=
Some
x
.
Proof
.
intros
->.
by
induction
l1
.
Qed
.
Lemma
nth_lookup_or_length
l
i
d
:
{
l
!!
i
=
Some
(
nth
i
l
d
)}
+
{(
length
l
≤
i
)%
nat
}.
Lemma
nth_lookup
l
i
d
:
nth
i
l
d
=
from_option
id
d
(
l
!!
i
).
Proof
.
revert
i
.
induction
l
as
[|
x
l
IH
]
;
intros
[|
i
]
;
simpl
;
auto
.
Qed
.
Lemma
nth_lookup_Some
l
i
d
x
:
l
!!
i
=
Some
x
→
nth
i
l
d
=
x
.
Proof
.
rewrite
nth_lookup
.
by
intros
->.
Qed
.
Lemma
nth_lookup_or_length
l
i
d
:
{
l
!!
i
=
Some
(
nth
i
l
d
)}
+
{
length
l
≤
i
}.
Proof
.
revert
i
;
induction
l
;
intros
i
.
-
right
.
simpl
.
omega
.
-
destruct
i
;
simpl
.
+
left
.
done
.
+
destruct
(
IHl
i
)
as
[->|]
;
[
by
left
|].
right
.
omega
.
Qed
.
Lemma
nth_lookup
l
i
d
x
:
l
!!
i
=
Some
x
→
nth
i
l
d
=
x
.
Proof
.
revert
i
;
induction
l
;
intros
i
;
[
done
|].
destruct
i
;
simpl
.
-
congruence
.
-
apply
IHl
.
rewrite
nth_lookup
.
destruct
(
l
!!
i
)
eqn
:
?
;
eauto
using
lookup_ge_None_1
.
Qed
.
Lemma
list_insert_alter
l
i
x
:
<[
i
:
=
x
]>
l
=
alter
(
λ
_
,
x
)
i
l
.
...
...
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