Theorems · Theorem · real analysis
HasDerivWithinAt.congr_of_mem
∀ {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) → x ∈ s → HasDerivWithinAt f₁ f' s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 5 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.
Cites6
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
- HasDerivWithinAt.congrproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAtproof · cited by 2
- not_differentiableAt_abs_zeroproof · cited by 2
- deriv2_sqrt_mul_logproof · cited by 1
- deriv_sqrt_mul_logproof · cited by 1