Theorems · Theorem · functional analysis
norm_nonneg
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), 0 ≤ ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 725 results in Mathlib
- Foundations
- Depth 112 from the axioms, rests on 2,425 definitions · 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.
- Realstatement and proof · cited by 25,697
- Norm.normstatement · cited by 5,413
- SeminormedAddGroupstatement and proof · cited by 331
- dist_zero_rightproof · cited by 172
- dist_nonnegproof · cited by 126
Cited by725
Results whose statement or proof uses this declaration.
- norm_normproof · cited by 113
- norm_eq_zeroproof · cited by 43
- ofReal_normproof · cited by 39
- abs_normproof · cited by 36
- MeasureTheory.dominatedFinMeasAdditive_cbmApplyMeasureproof · cited by 31
- MeasureTheory.norm_integral_le_integral_normproof · cited by 25
- closure_ballproof · cited by 20
- ContinuousLinearMap.isBoundedBilinearMapproof · cited by 18
- norm_le_pi_normproof · cited by 17
- ContinuousLinearMap.opNorm_comp_leproof · cited by 16
- orthonormal_iff_iteproof · cited by 15
- tendsto_pow_atTop_nhds_zero_of_norm_lt_oneproof · cited by 13
Showing the 200 most cited of 725.