Skip to content
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

Jump to bottom

[Merged by Bors] - feat: Add congr_deriv lemmas mirroring congr_fderiv #9065

Closed
wants to merge 2 commits into from
Closed

[Merged by Bors] - feat: Add congr_deriv lemmas mirroring congr_fderiv #9065

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
d32e895
congr_deriv
winstonyin Dec 15, 2023
21df766
Update Mathlib/Analysis/Calculus/Deriv/Basic.lean
winstonyin Dec 15, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Jump to
Jump to file
Failed to load files.
Diff view
Diff view
11 changes: 11 additions & 0 deletions Mathlib/Analysis/Calculus/Deriv/Basic.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -614,6 +614,17 @@ theorem Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem (h₁ : f₁ =ᶠ[𝓝[s
⟨fun h' ↦ h'.congr_of_eventuallyEq_of_mem h₁.symm hx,
fun h' ↦ h'.congr_of_eventuallyEq_of_mem h₁ hx⟩

theorem HasStrictDerivAt.congr_deriv (h : HasStrictDerivAt f f' x) (h' : f' = g') :
HasStrictDerivAt f g' x :=
h.congr_fderiv <| congr_arg _ h'

theorem HasDerivAt.congr_deriv (h : HasDerivAt f f' x) (h' : f' = g') : HasDerivAt f g' x :=
HasFDerivAt.congr_fderiv h <| congr_arg _ h'

theorem HasDerivWithinAt.congr_deriv (h : HasDerivWithinAt f f' s x) (h' : f' = g') :
HasDerivWithinAt f g' s x :=
HasFDerivWithinAt.congr_fderiv h <| congr_arg _ h'

theorem HasDerivAt.congr_of_eventuallyEq (h : HasDerivAt f f' x) (h₁ : f₁ =ᶠ[𝓝 x] f) :
HasDerivAt f₁ f' x :=
HasDerivAtFilter.congr_of_eventuallyEq h h₁ (mem_of_mem_nhds h₁ : _)
Expand Down