Theorems · Theorem · functional analysis
nnnorm_neg
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), ‖-a‖₊ = ‖a‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 114 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.
Cites5
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 · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- NNReal.eqproof · cited by 201
- norm_negproof · cited by 190
Cited by13
Results whose statement or proof uses this declaration.
- enorm_negproof · cited by 10
- nontrivialTopology_iff_exists_nnnorm_ne_zeroproof · cited by 4
- nndist_zero_rightproof · cited by 4
- MeasureTheory.SimpleFunc.norm_approxOn_zero_leproof · cited by 2
- MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_partproof · cited by 2
- MeasureTheory.Submartingale.upcrossings_ae_lt_top'proof · cited by 1
- Int.nnnorm_coe_unitsproof · cited by 1
- Real.lipschitzWith_cosproof · cited by 1
- IsUltrametricDist.nnnorm_intCast_le_oneproof · cited by 1
- ContinuousLinearMap.spectralRadius_eq_nnnormproof · cited by 1
- IsUltrametricDist.nnnorm_zsmul_leproof · cited by 1
- Polynomial.cauchyBound_X_sub_Cproof · cited by 0