Theorems · Theorem · real analysis
HasDerivWithinAt.congr
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f f₁ : 𝕜 → F} {f' : F} {x : 𝕜} {s : Set 𝕜},
HasDerivWithinAt f f' s x → (∀ x ∈ s, f₁ x = f x) → f₁ x = f x → HasDerivWithinAt f₁ f' s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 170 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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- HasDerivWithinAtstatement and proof · cited by 333
- Set.Subset.reflproof · cited by 66
- HasDerivWithinAt.congr_monoproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- HasDerivWithinAt.congr_of_memproof · cited by 5
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- Real.hasDerivWithinAt_arcsin_Iciproof · cited by 2
- Real.hasDerivWithinAt_arcsin_Iicproof · cited by 2
- Complex.deriv_Gamma_add_oneproof · cited by 1
- IntervalIntegrable.ae_hasDerivAt_integralproof · cited by 1
- convexOn_of_hasDerivWithinAt2_nonnegproof · cited by 0
- concaveOn_of_hasDerivWithinAt2_nonposproof · cited by 0