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
S
stdpp
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
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Simon Spies
stdpp
Commits
be4eb648
Commit
be4eb648
authored
Nov 26, 2018
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Versions of `elem_of_list_split` that give first or last element.
parent
f8f6d0a9
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
22 additions
and
0 deletions
+22
-0
theories/list.v
theories/list.v
+22
-0
No files found.
theories/list.v
View file @
be4eb648
...
...
@@ -647,6 +647,28 @@ Proof.
induction 1 as [x l|x y l ? [l1 [l2 ->]]]; [by eexists [], l|].
by exists (y :: l1), l2.
Qed.
Lemma elem_of_list_split_l `{EqDecision A} l x :
x ∈ l → ∃ l1 l2, l = l1 ++ x :: l2 ∧ x ∉ l1.
Proof.
induction 1 as [x l|x y l ? IH].
{ exists [], l. rewrite elem_of_nil. naive_solver. }
destruct (decide (x = y)) as [->|?].
- exists [], l. rewrite elem_of_nil. naive_solver.
- destruct IH as (l1 & l2 & -> & ?).
exists (y :: l1), l2. rewrite elem_of_cons. naive_solver.
Qed.
Lemma elem_of_list_split_r `{EqDecision A} l x :
x ∈ l → ∃ l1 l2, l = l1 ++ x :: l2 ∧ x ∉ l2.
Proof.
induction l as [|y l IH] using rev_ind.
{ by rewrite elem_of_nil. }
destruct (decide (x = y)) as [->|].
- exists l, []. rewrite elem_of_nil. naive_solver.
- rewrite elem_of_app, elem_of_list_singleton. intros [?| ->]; try done.
destruct IH as (l1 & l2 & -> & ?); auto.
exists l1, (l2 ++ [y]).
rewrite elem_of_app, elem_of_list_singleton, <-(assoc_L (++)). naive_solver.
Qed.
Lemma elem_of_list_lookup_1 l x : x ∈ l → ∃ i, l !! i = Some x.
Proof.
induction 1 as [|???? IH]; [by exists 0 |].
...
...
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