-
Notifications
You must be signed in to change notification settings - Fork 251
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
feat: port Analysis.Calculus.Deriv.Support (#4442)
- Loading branch information
Showing
2 changed files
with
55 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,54 @@ | ||
/- | ||
Copyright (c) 2022 Floris van Doorn. All rights reserved. | ||
Released under Apache 2.0 license as described in the file LICENSE. | ||
Authors: Floris van Doorn | ||
! This file was ported from Lean 3 source module analysis.calculus.deriv.support | ||
! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe | ||
! Please do not edit these lines, except to modify the commit id | ||
! if you have ported upstream changes. | ||
-/ | ||
import Mathlib.Analysis.Calculus.Deriv.Basic | ||
|
||
/-! | ||
# Support of the derivative of a function | ||
In this file we prove that the (topological) support of a function includes the support of its | ||
derivative. As a corollary, we show that the derivative of a function with compact support has | ||
compact support. | ||
## Keywords | ||
derivative, support | ||
-/ | ||
|
||
|
||
universe u v | ||
|
||
variable {π : Type u} [NontriviallyNormedField π] | ||
|
||
variable {E : Type v} [NormedAddCommGroup E] [NormedSpace π E] | ||
|
||
variable {f : π β E} | ||
|
||
/-! ### Support of derivatives -/ | ||
|
||
|
||
section Support | ||
|
||
open Function | ||
|
||
theorem support_deriv_subset : support (deriv f) β tsupport f := by | ||
intro x | ||
rw [β not_imp_not] | ||
intro h2x | ||
rw [not_mem_tsupport_iff_eventuallyEq] at h2x | ||
exact nmem_support.mpr (h2x.deriv_eq.trans (deriv_const x 0)) | ||
#align support_deriv_subset support_deriv_subset | ||
|
||
theorem HasCompactSupport.deriv (hf : HasCompactSupport f) : HasCompactSupport (deriv f) := | ||
hf.mono' support_deriv_subset | ||
#align has_compact_support.deriv HasCompactSupport.deriv | ||
|
||
end Support | ||
|