Theorems · Theorem · sequences and series
isUnit_one_sub_of_norm_lt_one
∀ {R : Type u_4} [inst : NormedRing R] [HasSummableGeomSeries R] {x : R}, ‖x‖ < 1 → IsUnit (1 - x)- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- IsUnitstatement · cited by 1,602
- NormedRingstatement and proof · cited by 924
- HasSummableGeomSeriesstatement and proof · cited by 60
- Units.oneSubproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- hasSum_coe_mul_geometric_of_norm_lt_one'proof · cited by 2