Theorems · Theorem · real analysis
DifferentiableAt.inverse
∀ {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 : NormedRing R] [HasSummableGeomSeries R]
[inst_5 : NormedAlgebra 𝕜 R] {h : E → R} {z : E},
DifferentiableAt 𝕜 h z → IsUnit (h z) → DifferentiableAt 𝕜 (fun x => Ring.inverse (h x)) z- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- IsUnitstatement and proof · cited by 1,602
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- DifferentiableAtstatement and proof · cited by 617
- Ring.inversestatement · cited by 160
- HasSummableGeomSeriesstatement and proof · cited by 60
- DifferentiableAt.compproof · cited by 38
- differentiableAt_inverseproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.inverseproof · cited by 0