Skip to content

at_left version of an at_right lemma #1255

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
affeldt-aist merged 2 commits into from
Jul 19, 2024
Merged

at_left version of an at_right lemma #1255

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
6a1c4a4
at_left version of an at_right lemma
affeldt-aist Jul 3, 2024
0d4ca11
rm duplicate
affeldt-aist Jul 5, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -36,6 +36,9 @@
- in `mathcomp_extra.v`:
+ lemmas `intr1D`, `intrD1`, `floor_eq`, `floorN`

- in `realfun.v`:
+ lemma `nondecreasing_at_left_is_cvgr`

### Changed

- in `topology.v`:
Expand Down
17 changes: 16 additions & 1 deletion theories/realfun.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -365,9 +365,24 @@ by eexists; apply: (@nondecreasing_at_right_cvgr _ _ (BLeft b));
[rewrite bnd_simp|near: b..].
Unshelve. all: by end_near. Qed.

Lemma nondecreasing_at_left_is_cvgr f a :
(\forall x \near a^'-, {in `]x, a[ &, {homo f : n m / n <= m}}) ->
(\forall x \near a^'-, has_ubound [set f y | y in `]x, a[]) ->
cvg (f x @[x --> a^'-]).
Proof.
move=> ndf ubf; suff: cvg ((f \o -%R) x @[x --> (- a)^'+]).
move=> /cvg_ex[/= l fal].
by apply/cvg_ex; exists l; exact/cvg_at_leftNP.
apply: @nonincreasing_at_right_is_cvgr.
- rewrite at_rightN near_simpl; apply: filterS ndf => x ndf y z.
by rewrite -2!oppr_itvoo => yxa zxa yz; rewrite ndf// lerNr opprK.
- rewrite at_rightN near_simpl; apply: filterS ubf => x [r ubf].
exists r => _/= [s sax <-]; rewrite ubf//=; exists (- s) => //.
by rewrite oppr_itvoo.
Qed.

End fun_cvg_realType.
Arguments nondecreasing_at_right_cvgr {R f a} b.
Arguments nondecreasing_at_right_cvgr {R f a} b.

Section fun_cvg_ereal.
Context {R : realType}.
Expand Down