Theorems · Theorem · functional analysis
NormedRing.inverse_one_sub_nth_order
∀ {R : Type u_1} [inst : NormedRing R] [HasSummableGeomSeries R] (n : ℕ),
∀ᶠ (t : R) in nhds 0, Ring.inverse (1 - t) = ∑ i ∈ Finset.range n, t ^ i + t ^ n * Ring.inverse (1 - t)- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- nhdsstatement · cited by 5,554
- Finset.sumstatement · cited by 5,195
- Filter.Eventuallystatement · cited by 3,134
- Dist.distproof · cited by 1,539
- Finset.rangestatement · cited by 1,341
- NormedRingstatement and proof · cited by 924
- dist_zero_rightproof · cited by 172
- Ring.inversestatement · cited by 160
- one_posproof · cited by 102
- HasSummableGeomSeriesstatement and proof · cited by 60
- Metric.eventually_nhds_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- NormedRing.inverse_add_nth_orderproof · cited by 1