Theorems · Theorem · functional analysis
nnnorm_ne_zero_iff
∀ {E : Type u_5} [inst : NormedAddGroup E] {a : E}, ‖a‖₊ ≠ 0 ↔ a ≠ 0- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddGroup
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
- Iff.notproof · cited by 489
- NormedAddGroupstatement and proof · cited by 32
- nnnorm_eq_zeroproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.exists_lt_apply_of_lt_opNNNormproof · cited by 3
- MeasureTheory.VectorMeasure.variation_smulproof · cited by 2
- hasFPowerSeriesAt_iffproof · cited by 1
- Bornology.IsVonNBounded.restrict_scalars_of_nontrivialproof · cited by 1
- spectrum.isUnit_one_sub_smul_of_lt_inv_radiusproof · cited by 1
- nnnorm_posproof · cited by 1