Theorems · Theorem · field theory
nnnorm_commutator_sub_one_le
∀ {α : Type u_2} [inst : NormedDivisionRing α] {a b : α},
a ≠ 0 → b ≠ 0 → ‖a * b * a⁻¹ * b⁻¹ - 1‖₊ ≤ 2 * ‖a‖₊⁻¹ * ‖b‖₊⁻¹ * ‖a - 1‖₊ * ‖b - 1‖₊- Defined in
- Mathlib.Analysis.Normed.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement and proof · cited by 952
- NormedDivisionRingstatement and proof · cited by 360
- Units.mk0proof · cited by 181
- Units.val_inv_eq_inv_valproof · cited by 57
- nnnorm_invproof · cited by 14
- nnnorm_commutator_units_sub_one_leproof · cited by 1
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