Theorems · Theorem · functional analysis
nnnorm_commutator_units_sub_one_le
∀ {α : Type u_2} [inst : SeminormedRing α] (a b : αˣ),
‖↑(a * b * a⁻¹ * b⁻¹) - 1‖₊ ≤ 2 * ‖↑a⁻¹‖₊ * ‖↑b⁻¹‖₊ * ‖↑a - 1‖₊ * ‖↑b - 1‖₊- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRing
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.
- NNRealstatement · cited by 4,310
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- NNNorm.nnnormstatement · cited by 952
- SeminormedRingstatement and proof · cited by 446
- norm_commutator_units_sub_one_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- nnnorm_commutator_sub_one_leproof · cited by 0