Theorems · Theorem · field theory
nnnorm_inv
∀ {α : Type u_2} [inst : NormedDivisionRing α] (a : α), ‖a⁻¹‖₊ = ‖a‖₊⁻¹- Defined in
- Mathlib.Analysis.Normed.Field.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
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.
- Norm.normproof · cited by 5,413
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- NormedDivisionRingstatement and proof · cited by 360
- NNReal.eqproof · cited by 201
- norm_invproof · cited by 126
Cited by14
Results whose statement or proof uses this declaration.
- enorm_invproof · cited by 7
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- MeasureTheory.Measure.hausdorffMeasure_smul₀proof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- MeasureTheory.VectorMeasure.variation_smulproof · cited by 2
- egauge_le_of_smul_mem_of_neproof · cited by 2
- MeasureTheory.hausdorffMeasure_homothety_preimageproof · cited by 2
- ContinuousLinearMap.exists_nnnorm_eq_one_lt_apply_of_lt_opNNNormproof · cited by 1
- le_egauge_smul_rightproof · cited by 1
- Polynomial.mahlerMeasure_C_mul_X_add_Cproof · cited by 1
- spectrum.isUnit_one_sub_smul_of_lt_inv_radiusproof · cited by 1
- ediam_smul₀proof · cited by 1