Theorems · Theorem · functional analysis
nnnorm_pos
∀ {E : Type u_5} [inst : NormedAddGroup E] {a : E}, 0 < ‖a‖₊ ↔ a ≠ 0- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 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
- pos_iff_ne_zeroproof · cited by 180
- NormedAddGroupstatement and proof · cited by 32
- nnnorm_ne_zero_iffproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- ediam_smul₀proof · cited by 1