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feat(geometry/manifold/mfderiv): more lemmas (#6679)
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* move section `mfderiv_fderiv` up, add aliases;
* rename old `unique_mdiff_on.unique_diff_on` to `unique_mdiff_on.unique_diff_on_target_inter`;
* add a section about `continuous_linear_map`;
* more lemmas about `model_with_corners`;
* add lemmas about `ext_chart_at`.
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urkud committed Mar 16, 2021
1 parent 214b8e8 commit a116025
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4 changes: 4 additions & 0 deletions src/analysis/calculus/fderiv.lean
Expand Up @@ -650,6 +650,10 @@ lemma has_fderiv_within_at.congr (h : has_fderiv_within_at f f' s x) (hs : ∀x
(hx : f₁ x = f x) : has_fderiv_within_at f₁ f' s x :=
h.congr_mono hs hx (subset.refl _)

lemma has_fderiv_within_at.congr' (h : has_fderiv_within_at f f' s x) (hs : ∀x ∈ s, f₁ x = f x)
(hx : x ∈ s) : has_fderiv_within_at f₁ f' s x :=
h.congr hs (hs x hx)

lemma has_fderiv_within_at.congr_of_eventually_eq (h : has_fderiv_within_at f f' s x)
(h₁ : f₁ =ᶠ[𝓝[s] x] f) (hx : f₁ x = f x) : has_fderiv_within_at f₁ f' s x :=
has_fderiv_at_filter.congr_of_eventually_eq h h₁ hx
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