Theorems · Theorem · functional analysis
enorm_neg
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), ‖-a‖ₑ = ‖a‖ₑ- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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.
- ENNRealstatement · cited by 9,879
- ENNReal.ofNNRealproof · cited by 1,279
- NNNorm.nnnormproof · cited by 952
- ENorm.enormstatement · cited by 715
- SeminormedAddGroupstatement and proof · cited by 331
- nnnorm_negproof · cited by 13
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_negproof · cited by 15
- isCompact_setOfPred_finiteMeasure_le_of_compactSpaceproof · cited by 3
- MeasureTheory.VectorMeasure.variation_negproof · cited by 3
- MeasureTheory.HasFiniteIntegral.negproof · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- enorm_sub_revproof · cited by 2
- Manifold.pathELength_comp_of_antitoneOnproof · cited by 1
- MeasureTheory.eLpNorm'_negproof · cited by 1
- MeasureTheory.lintegral_enorm_negproof · cited by 0
- tendsto_zero_iff_enorm_tendsto_zeroproof · cited by 0