Theorems · Theorem · real analysis
DifferentiableAt.fun_inv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {R : Type u_5} [inst_3 : NormedDivisionRing R] [inst_4 : NormedAlgebra 𝕜 R] {h : E → R}
{z : E}, DifferentiableAt 𝕜 h z → h z ≠ 0 → DifferentiableAt 𝕜 (fun i => (h i)⁻¹) zEta-expanded form of DifferentiableAt.inv
- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 183 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.
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- NontriviallyNormedFieldstatement · cited by 8,742
- NormedAlgebrastatement · cited by 1,165
- DifferentiableAtstatement · cited by 617
- NormedDivisionRingstatement · cited by 360
- DifferentiableAt.invproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Chebyshev.primeCounting_eq_theta_div_log_add_integralproof · cited by 2
- Real.differentiableAt_binEntropy_iff_ne_zero_oneproof · cited by 1
- deriv_riemannZeta_eq_neg_inv_sub_sq_addproof · cited by 1
- Real.differentiableAt_inv_logproof · cited by 1
- deriv_riemannZeta_eq_neg_inv_sub_sq_mul_addproof · cited by 0