Theorems · Theorem · group theory
Finset.sum_cons
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} {a : ι} [inst : AddCommMonoid M] {f : ι → M} (h : a ∉ s),
∑ x ∈ Finset.cons a s h, f x = f a + ∑ x ∈ s, f x- Cited by
- 84 results in Mathlib
- Foundations
- Depth 58 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Finset.consstatement · cited by 221
- Finset.fold_consproof · cited by 6
Cited by84
Results whose statement or proof uses this declaration.
- Finset.prod_pow_eq_pow_sumproof · cited by 18
- Polynomial.degree_sum_leproof · cited by 11
- IsNonarchimedean.apply_sum_le_supproof · cited by 6
- Finset.add_sum_Ioc_eq_sum_Iccproof · cited by 5
- Nat.prod_factorial_dvd_factorial_sumproof · cited by 5
- logDeriv_prodproof · cited by 4
- Finset.sum_insertNoneproof · cited by 4
- MeasureTheory.integral_finsetSum_measureproof · cited by 4
- Finset.Nonempty.norm_sum_le_sup'_normproof · cited by 4
- Finsupp.support_finsetSumproof · cited by 3
- StrictConvexOn.map_sum_ltproof · cited by 3
- Commute.add_pow_prime_pow_eq'proof · cited by 3