Theorems · Theorem · functional analysis
dist_sum_sum_le
∀ {ι : Type u_3} {E : Type u_5} [inst : SeminormedAddCommGroup E] (s : Finset ι) (f a : ι → E),
dist (∑ b ∈ s, f b) (∑ b ∈ s, a b) ≤ ∑ b ∈ s, dist (f b) (a b)- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement · cited by 5,195
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_rflproof · cited by 1,558
- Dist.diststatement · cited by 1,539
- dist_sum_sum_le_of_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- dist_birkhoffSum_birkhoffSum_leproof · cited by 1