Theorems · Theorem · real analysis
AntitoneOn.sum_le_integral_Ico
∀ {a b : ℕ} {f : ℝ → ℝ},
a ≤ b → AntitoneOn f (Set.Icc ↑a ↑b) → ∑ i ∈ Finset.Ico a b, f ↑(i + 1) ≤ ∫ (x : ℝ) in ↑a..↑b, f x- Defined in
- Mathlib.Analysis.SumIntegralComparisons
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finset.sumstatement and proof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Set.Iccstatement and proof · cited by 1,702
- Finset.rangeproof · cited by 1,341
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- add_assocproof · cited by 746
- Nat.cast_addproof · cited by 586
- intervalIntegralstatement and proof · cited by 546
- Finset.Icostatement and proof · cited by 450
Cited by3
Results whose statement or proof uses this declaration.
- AntitoneOn.sum_Ico_le_integralproof · cited by 3
- harmonic_le_one_add_logproof · cited by 1
- MonotoneOn.integral_le_sum_Icoproof · cited by 0