Theorems · Theorem · group theory
Finset.sum_Ico_consecutive
∀ {M : Type u_3} [inst : AddCommMonoid M] (f : ℕ → M) {m n k : ℕ},
m ≤ n → n ≤ k → ∑ i ∈ Finset.Ico m n, f i + ∑ i ∈ Finset.Ico n k, f i = ∑ i ∈ Finset.Ico m k, f i- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Finset.Icostatement · cited by 450
- Finset.sum_unionproof · cited by 40
- Finset.Ico_union_Ico_eq_Icoproof · cited by 7
- Finset.Ico_disjoint_Ico_consecutiveproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Finset.sum_range_add_sum_Icoproof · cited by 12
- eVariationOn.unionproof · cited by 4
- Finset.sum_schlomilch_le'proof · cited by 2
- Finset.le_sum_schlomilch'proof · cited by 2
- Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digitsproof · cited by 1
- Nat.Prime.emultiplicity_factorial_mul_succproof · cited by 1
- eVariationOn.add_pointproof · cited by 1
- FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2proof · cited by 1
- MeasureTheory.upcrossingsBefore_eq_sumproof · cited by 1
- Nat.factorization_factorial_mul_succproof · cited by 1