Theorems · Theorem · general topology
IsUltrametricDist.nnnorm_sum_eq_sup_of_pairwise_ne
∀ {M : Type u_1} {ι : Type u_2} [inst : SeminormedAddCommGroup M] [IsUltrametricDist M] {s : Finset ι} {f : ι → M},
((↑s).Pairwise fun i j => ‖f i‖₊ ≠ ‖f j‖₊) → ‖∑ i ∈ s, f i‖₊ = s.sup fun i => ‖f i‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Finset.Nonemptyproof · cited by 1,001
- NNNorm.nnnormstatement and proof · cited by 952
- Finset.supstatement and proof · cited by 530
- Set.Pairwisestatement and proof · cited by 321
- Finset.sum_singletonproof · cited by 251
- Finset.consproof · cited by 221
- IsUltrametricDiststatement and proof · cited by 177
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.norm_sum_eq_sup'_of_pairwise_neproof · cited by 0