Theorems · Theorem · group theory
Finset.sum_Ico_succ_top
∀ {M : Type u_3} [inst : AddCommMonoid M] {a b : ℕ},
a ≤ b → ∀ (f : ℕ → M), ∑ k ∈ Finset.Ico a (b + 1), f k = ∑ k ∈ Finset.Ico a b, f k + f b- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 6 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.
Cites8
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
- add_commproof · cited by 1,535
- Finset.Icostatement and proof · cited by 450
- Finset.sum_insertproof · cited by 196
- Finset.right_notMem_Icoproof · cited by 13
- Finset.insert_Ico_right_eq_Ico_add_oneproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- intervalIntegral.sum_integral_adjacent_intervals_Icoproof · cited by 4
- Finset.sum_Ico_succ_sub_topproof · cited by 1
- Nat.factorization_factorial_mul_succproof · cited by 1
- discrete_gronwall_prod_generalproof · cited by 1
- Nat.Prime.emultiplicity_factorial_mul_succproof · cited by 1
- Finset.sum_Icc_succ_topproof · cited by 0