Theorems · Theorem · functional analysis
nnnorm_multiset_sum_le
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (m : Multiset E), ‖m.sum‖₊ ≤ (Multiset.map (fun x => ‖x‖₊) m).sum- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Norm.normproof · cited by 5,413
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Multisetstatement and proof · cited by 2,627
- NNReal.toRealproof · cited by 1,260
- NNNorm.nnnormstatement and proof · cited by 952
- Multiset.mapstatement and proof · cited by 876
- Multiset.sumstatement and proof · cited by 388
- Multiset.map_mapproof · cited by 151
- NNReal.coe_le_coeproof · cited by 73
- norm_multiset_sum_leproof · cited by 3
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