Theorems · Theorem · functional analysis
eq_zero_or_norm_pos
∀ {E : Type u_5} [inst : NormedAddGroup E] (a : E), a = 0 ∨ 0 < ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 116 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- norm_nonnegproof · cited by 725
- LE.le.eq_or_ltproof · cited by 220
- norm_pos_iffproof · cited by 168
- norm_eq_zeroproof · cited by 43
- NormedAddGroupstatement and proof · cited by 32
Cited by6
Results whose statement or proof uses this declaration.
- CStarAlgebra.span_nonneg_inter_closedBallproof · cited by 2
- eq_zero_or_nnnorm_posproof · cited by 2
- CStarRing.of_le_norm_mul_star_selfproof · cited by 0
- PositiveLinearMap.exists_norm_apply_leproof · cited by 0
- CStarMatrix.norm_entry_le_normproof · cited by 0
- AnalyticOnNhd.sum_divisor_leproof · cited by 0