Theorems · Theorem · several complex variables
analyticOnNhd_inverse
∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {A : Type u_7} [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[HasSummableGeomSeries A], AnalyticOnNhd 𝕜 Ring.inverse {x | IsUnit x}- Defined in
- Mathlib.Analysis.Analytic.Constructions
- 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.
Cites10
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
- Set.ofPredstatement and proof · cited by 6,101
- IsUnitstatement and proof · cited by 1,602
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- IsUnit.unitproof · cited by 252
- AnalyticOnNhdstatement · cited by 206
- Ring.inversestatement · cited by 160
- HasSummableGeomSeriesstatement and proof · cited by 60
- analyticAt_inverseproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- contDiffAt_ringInverseproof · cited by 2