Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
R
rtproofs
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Sophie Quinton
rtproofs
Commits
76263149
Commit
76263149
authored
Nov 03, 2016
by
Felipe Cerqueira
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Add more lemmas about zip
parent
af7806cd
Changes
1
Show whitespace changes
Inline
Sidebyside
Showing
1 changed file
with
54 additions
and
0 deletions
+54
0
util/list.v
util/list.v
+54
0
No files found.
util/list.v
View file @
76263149
...
...
@@ 228,6 +228,60 @@ Section Zip.
}
Qed
.
Lemma
unzip1_pair
:
forall
{
T1
T2
:
eqType
}
(
l
:
seq
T1
)
(
f
:
T1
>
T2
),
unzip1
[
seq
(
x
,
f
x
)

x
<
l
]
=
l
.
Proof
.
intros
T1
T2
.
induction
l
;
first
by
done
.
by
intros
f
;
simpl
;
f_equal
.
Qed
.
Lemma
unzip2_pair
:
forall
{
T1
T2
:
eqType
}
(
l
:
seq
T1
)
(
f
:
T1
>
T2
),
unzip2
[
seq
(
f
x
,
x
)

x
<
l
]
=
l
.
Proof
.
intros
T1
T2
.
induction
l
;
first
by
done
.
by
intros
f
;
simpl
;
f_equal
.
Qed
.
Lemma
eq_unzip1
:
forall
{
T1
T2
:
eqType
}
(
l1
l2
:
seq
(
T1
*
T2
))
x0
,
size
l1
=
size
l2
>
(
forall
i
,
i
<
size
l1
>
(
fst
(
nth
x0
l1
i
))
=
(
fst
(
nth
x0
l2
i
)))
>
unzip1
l1
=
unzip1
l2
.
Proof
.
intros
T1
T2
.
induction
l1
;
simpl
;
first
by
destruct
l2
.
intros
l2
x0
SIZE
ALL
.
destruct
l2
;
first
by
done
.
simpl
;
f_equal
;
first
by
feed
(
ALL
0
).
case
:
SIZE
=>
SIZE
.
apply
IHl1
with
(
x0
:
=
x0
)
;
first
by
done
.
intros
i
LTi
.
by
feed
(
ALL
i
.+
1
)
;
first
by
rewrite
[
X
in
X
<
_
]
addn1
[
X
in
_
<
X
]
addn1
ltn_add2r
.
Qed
.
Lemma
eq_unzip2
:
forall
{
T1
T2
:
eqType
}
(
l1
l2
:
seq
(
T1
*
T2
))
x0
,
size
l1
=
size
l2
>
(
forall
i
,
i
<
size
l1
>
(
snd
(
nth
x0
l1
i
))
=
(
snd
(
nth
x0
l2
i
)))
>
unzip2
l1
=
unzip2
l2
.
Proof
.
intros
T1
T2
.
induction
l1
;
simpl
;
first
by
destruct
l2
.
intros
l2
x0
SIZE
ALL
.
destruct
l2
;
first
by
done
.
simpl
;
f_equal
;
first
by
feed
(
ALL
0
).
case
:
SIZE
=>
SIZE
.
apply
IHl1
with
(
x0
:
=
x0
)
;
first
by
done
.
intros
i
LTi
.
by
feed
(
ALL
i
.+
1
)
;
first
by
rewrite
[
X
in
X
<
_
]
addn1
[
X
in
_
<
X
]
addn1
ltn_add2r
.
Qed
.
End
Zip
.
(* Restate nth_error function from Coq library. *)
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment