Theorems · Theorem · number theory
not_summable_indicator_mod_of_antitone_of_neg
∀ {m : ℕ} [hm : NeZero m] {f : ℕ → ℝ},
Antitone f → ∀ {n : ℕ}, f n < 0 → ∀ (k : ZMod m), ¬Summable ({n | ↑n = k}.indicator f)If f : ℕ → ℝ is decreasing and has a negative term, then f restricted to a residue
class is not summable.
- Defined in
- Mathlib.Analysis.SumOverResidueClass
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ZModstatement and proof · cited by 1,024
- LE.le.trans_ltproof · cited by 795
- Summablestatement and proof · cited by 778
- Set.indicatorstatement and proof · cited by 723
- Antitonestatement and proof · cited by 563
- ZMod.valproof · cited by 159
- ZMod.natCast_zmod_valproof · cited by 29
- Antitone.comp_monotoneproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- summable_indicator_mod_iff_summable_indicator_modproof · cited by 1