Theorems · Theorem · real analysis
differentiableAt_inverse
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {R : Type u_5} [inst_1 : NormedRing R] [HasSummableGeomSeries R]
[inst_3 : NormedAlgebra 𝕜 R] {x : R}, IsUnit x → DifferentiableAt 𝕜 Ring.inverse x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 4 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- 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 and proof · cited by 160
- HasFDerivAt.differentiableAtproof · cited by 83
- HasSummableGeomSeriesstatement and proof · cited by 60
- hasFDerivAt_ringInverseproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- DifferentiableWithinAt.inverseproof · cited by 1
- differentiableWithinAt_inverseproof · cited by 1
- spectrum.differentiableOn_inverse_one_sub_smulproof · cited by 1
- DifferentiableAt.inverseproof · cited by 1