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Merge master into nightly-testing
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leanprover-community-mathlib4-bot committed Dec 17, 2023
2 parents c557306 + b835302 commit 922483d
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7 changes: 7 additions & 0 deletions Mathlib/Geometry/Manifold/MFDeriv.lean
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Expand Up @@ -821,6 +821,13 @@ theorem MDifferentiable.prod_mk_space {f : M → E'} {g : M → E''} (hf : MDiff

/-! ### Congruence lemmas for derivatives on manifolds -/

theorem HasMFDerivAt.congr_mfderiv (h : HasMFDerivAt I I' f x f') (h' : f' = f₁') :
HasMFDerivAt I I' f x f₁' :=
h' ▸ h

theorem HasMFDerivWithinAt.congr_mfderiv (h : HasMFDerivWithinAt I I' f s x f') (h' : f' = f₁') :
HasMFDerivWithinAt I I' f s x f₁' :=
h' ▸ h

theorem HasMFDerivWithinAt.congr_of_eventuallyEq (h : HasMFDerivWithinAt I I' f s x f')
(h₁ : f₁ =ᶠ[𝓝[s] x] f) (hx : f₁ x = f x) : HasMFDerivWithinAt I I' f₁ s x f' := by
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