Theorems · Theorem · global analysis
DifferentiableOn.congr
∀ {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} {s : Set E},
DifferentiableOn 𝕜 f s → (∀ x ∈ s, f₁ x = f x) → DifferentiableOn 𝕜 f₁ s- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Congr
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- DifferentiableOnstatement and proof · cited by 419
- DifferentiableWithinAt.congrproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- differentiable_riemannZeta₀proof · cited by 5
- differentiableOn_congrproof · cited by 3
- differentiableAt_iteratedDerivWithin_cexpproof · cited by 2
- EisensteinSeries.eisSummand_extension_differentiableOnproof · cited by 1
- DirichletCharacter.differentiable_LFunctionTrivChar₁proof · cited by 1
- ModularForm.differentiableOn_tprod_one_sub_pow_powproof · cited by 1
- SummableLocallyUniformlyOn.differentiableOnproof · cited by 1
- E2_mdifferentiableproof · cited by 1
- Derivative.normalizedDerivOfComplex_mdifferentiableproof · cited by 1
- differentiableOn_iteratedDerivWithin_cotTermproof · cited by 0