Theorems · Theorem · group theory
Finset.sum_eq_add_sum_sdiff_singleton_of_mem
∀ {ι : Type u_1} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : DecidableEq ι] {s : Finset ι} {i : ι},
i ∈ s → ∀ (f : ι → M), ∑ x ∈ s, f x = f i + ∑ x ∈ s \ {i}, f x- Cited by
- 9 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
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
- IsEmpty.forall_iffproof · cited by 39
- Finset.sum_eq_add_sum_sdiff_singletonproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Finset.sum_eq_sum_sdiff_singleton_addproof · cited by 5
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- Finsupp.le_weightproof · cited by 1
- Finsupp.le_weight_of_ne_zeroproof · cited by 1
- Valuation.map_sum_eq_of_ltproof · cited by 1
- Fintype.sum_eq_add_sum_complproof · cited by 1
- WittVector.dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeffproof · cited by 1
- bernoulli_spec'proof · cited by 1
- Finset.sum_eq_sum_iff_singleproof · cited by 0