Theorems · Theorem · functional analysis
NormedRing.inverse_one_sub
∀ {R : Type u_1} [inst : NormedRing R] [inst_1 : HasSummableGeomSeries R] (t : R) (h : ‖t‖ < 1),
Ring.inverse (1 - t) = ↑(Units.oneSub t h)⁻¹- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 168 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.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Unitsstatement · cited by 2,804
- Units.valstatement · cited by 1,966
- NormedRingstatement and proof · cited by 924
- Ring.inversestatement and proof · cited by 160
- HasSummableGeomSeriesstatement and proof · cited by 60
- Ring.inverse_unitproof · cited by 24
- Units.oneSubstatement and proof · cited by 9
- Units.val_oneSubproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- hasFPowerSeriesOnBall_inverse_one_subproof · cited by 3
- NormedRing.inverse_one_sub_normproof · cited by 2
- NormedRing.inverse_one_sub_nth_order'proof · cited by 1
- spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smulproof · cited by 1