Theorems · Theorem · group theory
Finset.sum_Icc_succ_eq_add_endpoints
∀ {R : Type u_1} [inst : AddCommGroup R] (f : ℤ → R) {N : ℕ},
∑ m ∈ Finset.Icc (-(↑N + 1)) (↑N + 1), f m = f (↑N + 1) + f (-(↑N + 1)) + ∑ m ∈ Finset.Icc (-↑N) ↑N, f m- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Finset.sumstatement and proof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Disjointproof · cited by 2,201
- Nat.cast_addproof · cited by 586
- Finset.Iccstatement and proof · cited by 348
- neg_add_revproof · cited by 236
- Finset.sum_unionproof · cited by 40
- Finset.mem_Iccproof · cited by 39
- le_add_iff_nonneg_leftproof · cited by 12
- Finset.disjoint_singleton_rightproof · cited by 12
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