Theorems · Theorem · functional analysis
norm_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
- 2 results in Mathlib
- Foundations
- Depth 115 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Unitsstatement and proof · cited by 2,804
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Units.valstatement and proof · cited by 1,966
- norm_nonnegproof · cited by 725
- add_le_addproof · cited by 666
- neg_zeroproof · cited by 542
- SeminormedRingstatement and proof · cited by 446
- mul_le_mul_of_nonneg_rightproof · cited by 301
- sub_mulproof · cited by 170
Cited by2
Results whose statement or proof uses this declaration.
- nnnorm_commutator_units_sub_one_leproof · cited by 1
- norm_commutator_sub_one_leproof · cited by 0