Theorems · Theorem · global analysis
DifferentiableWithinAt.congr_of_eventuallyEq
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f f₁ : E → F} {x : E} {s : Set E},
DifferentiableWithinAt 𝕜 f s x → f₁ =ᶠ[nhdsWithin x s] f → f₁ x = f x → DifferentiableWithinAt 𝕜 f₁ s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Congr
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsWithinstatement and proof · cited by 1,912
- Filter.EventuallyEqstatement and proof · cited by 1,912
- DifferentiableWithinAtstatement and proof · cited by 453
- DifferentiableWithinAt.hasFDerivWithinAtproof · cited by 132
- HasFDerivWithinAt.differentiableWithinAtproof · cited by 65
- HasFDerivWithinAt.congr_of_eventuallyEqproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- MonotoneOn.ae_differentiableWithinAt_of_memproof · cited by 3
- ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithinproof · cited by 3
- differentiableWithinAt_smul_iffproof · cited by 2
- differentiableWithinAt_dslope_of_neproof · cited by 2
- DifferentiableWithinAt.congr_of_eventuallyEq_of_memproof · cited by 1
- VectorField.DifferentiableWithinAt.pullbackWithinproof · cited by 0