Theorems · Theorem · group theory
Finset.sum_Ioc_consecutive
∀ {M : Type u_3} [inst : AddCommMonoid M] (f : ℕ → M) {m n k : ℕ},
m ≤ n → n ≤ k → ∑ i ∈ Finset.Ioc m n, f i + ∑ i ∈ Finset.Ioc n k, f i = ∑ i ∈ Finset.Ioc m k, f i- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 1 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- LT.lt.trans_leproof · cited by 678
- Finset.Iocstatement and proof · cited by 301
- lt_irreflproof · cited by 190
- Finset.disjoint_leftproof · cited by 50
- Finset.sum_unionproof · cited by 40
- Finset.mem_Iocproof · cited by 26
- Finset.Ioc_union_Ioc_eq_Iocproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_Ioc_succ_topproof · cited by 1