Theorems · Theorem · functional analysis
dist_sum_sum_le_of_le
∀ {ι : Type u_3} {E : Type u_5} [inst : SeminormedAddCommGroup E] (s : Finset ι) {f a : ι → E} {d : ι → ℝ},
(∀ b ∈ s, dist (f b) (a b) ≤ d b) → dist (∑ b ∈ s, f b) (∑ b ∈ s, a b) ≤ ∑ b ∈ s, d b- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 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 and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Norm.normproof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement and proof · cited by 1,539
- Finset.sum_add_distribproof · cited by 131
- Finset.sum_neg_distribproof · cited by 65
- dist_eq_norm_neg_addproof · cited by 46
- norm_sum_le_of_leproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleOproof · cited by 2
- MeasureTheory.IntegrableOn.hasBoxIntegralproof · cited by 2
- dist_sum_sum_leproof · cited by 1