Theorems · Theorem · functional analysis
Units.val_add
∀ {R : Type u_1} [inst : NormedRing R] [inst_1 : HasSummableGeomSeries R] (x : Rˣ) (t : R) (h : ‖t‖ < ‖↑x⁻¹‖⁻¹),
↑(x.add t h) = ↑x + t- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 2 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.
Cites7
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 and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- NormedRingstatement and proof · cited by 924
- HasSummableGeomSeriesstatement and proof · cited by 60
- Units.addstatement and proof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- spectrum.mem_resolventSet_of_norm_lt_mulproof · cited by 3
- NormedRing.inverse_addproof · cited by 2