Theorems · Theorem · functional analysis
norm_multiset_sum_le
∀ {E : Type u_9} [inst : SeminormedAddCommGroup E] (m : Multiset E), ‖m.sum‖ ≤ (Multiset.map (fun x => ‖x‖) m).sum- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement · cited by 876
- Eq.leproof · cited by 605
- Multiset.sumstatement · cited by 388
- norm_zeroproof · cited by 366
- norm_add_leproof · cited by 68
- Multiset.le_sum_of_subadditiveproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- PiTensorProduct.norm_eval_le_projectiveSeminormproof · cited by 2
- Polynomial.coeff_le_of_roots_leproof · cited by 1
- nnnorm_multiset_sum_leproof · cited by 0