Theorems · Theorem · functional analysis
NormedSpace.invOf_exp_of_mem_ball
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕂] [inst_1 : NormedRing 𝔸] [inst_2 : NormedAlgebra 𝕂 𝔸]
[CompleteSpace 𝔸] [CharZero 𝕂] {x : 𝔸},
x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝔸).radius →
∀ [inst : Invertible (NormedSpace.exp x)], ⅟(NormedSpace.exp x) = NormedSpace.exp (-x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- CharZerostatement and proof · cited by 932
- NormedRingstatement and proof · cited by 924
- Invertiblestatement and proof · cited by 549
- Metric.eballstatement and proof · cited by 294
- Invertible.invOfstatement and proof · cited by 268
- NormedSpace.expstatement and proof · cited by 157
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- NormedSpace.expSeriesstatement and proof · cited by 68
Cited by1
Results whose statement or proof uses this declaration.
- NormedSpace.invOf_expproof · cited by 0