Theorems · Theorem · group theory
Finset.sum_range_eq_add_Ico
∀ {M : Type u_3} [inst : AddCommMonoid M] (f : ℕ → M) {n : ℕ},
0 < n → ∑ x ∈ Finset.range n, f x = f 0 + ∑ x ∈ Finset.Ico 1 n, f x- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 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.rangestatement · cited by 1,341
- Finset.Icostatement · cited by 450
- Finset.range_eq_Icoproof · cited by 26
- Finset.sum_eq_sum_Ico_succ_botproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Nat.Partition.hasProd_powerSeriesMk_card_countRestrictedproof · cited by 2
- PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sqproof · cited by 1