Theorems · Theorem · real analysis
fderiv_inverse
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {R : Type u_5} [inst_1 : NormedRing R] [HasSummableGeomSeries R]
[inst_3 : NormedAlgebra 𝕜 R] (x : Rˣ), fderiv 𝕜 Ring.inverse ↑x = -((ContinuousLinearMap.mulLeftRight 𝕜 R) ↑x⁻¹) ↑x⁻¹- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- fderivstatement · cited by 398
- Ring.inversestatement · cited by 160
- HasFDerivAt.fderivproof · cited by 93
- HasSummableGeomSeriesstatement and proof · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- hasStrictFDerivAt_ringInverseproof · cited by 1