Theorems · Theorem · real analysis
hasStrictFDerivAt_ringInverse
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {R : Type u_5} [inst_1 : NormedRing R] [HasSummableGeomSeries R]
[inst_3 : NormedAlgebra 𝕜 R] (x : Rˣ),
HasStrictFDerivAt Ring.inverse (-((ContinuousLinearMap.mulLeftRight 𝕜 R) ↑x⁻¹) ↑x⁻¹) ↑x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- fderivproof · cited by 398
Cited by1
Results whose statement or proof uses this declaration.
- hasStrictFDerivAt_inv'proof · cited by 0