Theorems · Theorem · group theory
Finset.sum_Icc_eq_sum_Ico_add
∀ {α : Type u_1} [inst : AddCommMonoid α] (f : ℤ → α) {l u : ℤ},
l ≤ u → ∑ m ∈ Finset.Icc l u, f m = ∑ m ∈ Finset.Ico l u, f m + f u- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
Cites12
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 and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- add_commproof · cited by 1,535
- Finset.Icostatement and proof · cited by 450
- Finset.Iccstatement · cited by 348
- Finset.sum_insertproof · cited by 196
- Finset.cons_eq_insertproof · cited by 59
- Finset.mem_Icoproof · cited by 50
- lt_self_iff_falseproof · cited by 41
- Finset.right_notMem_Icoproof · cited by 13
- Finset.Icc_eq_cons_Icoproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- HasSum.hasSum_symmetricIco_of_hasSum_symmetricIccproof · cited by 3