Theorems · Theorem · general topology
IsUltrametricDist.exists_norm_finset_sum_le_of_nonempty
Deprecated since 2026-04-08Use IsUltrametricDist.exists_norm_finsetSum_le_of_nonempty instead.
∀ {M : Type u_1} {ι : Type u_2} [inst : SeminormedAddCommGroup M] [IsUltrametricDist M] {t : Finset ι},
t.Nonempty → ∀ (f : ι → M), ∃ i ∈ t, ‖∑ j ∈ t, f j‖ ≤ ‖f i‖Alias of IsUltrametricDist.exists_norm_finsetSum_le_of_nonempty.
Given a function f : ι → M and a nonempty finite set t ⊆ ι, we can always find
i ∈ t such that ‖∑ j ∈ t, f j‖ ≤ ‖f i‖.
- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Finsetstatement · cited by 13,712
- Norm.normstatement · cited by 5,413
- Finset.sumstatement · cited by 5,195
- SeminormedAddCommGroupstatement · cited by 2,671
- Finset.Nonemptystatement · cited by 1,001
- IsUltrametricDiststatement · cited by 177
- IsUltrametricDist.exists_norm_finsetSum_le_of_nonemptyproof · cited by 2
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