Theorems · Theorem · group theory
Finset.sum_update_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) (b : M), ∑ x ∈ s, Function.update f i b x = b + ∑ x ∈ s \ {i}, f x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 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.
Cites11
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 and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Function.updatestatement · cited by 502
- Finset.sum_constproof · cited by 254
- Finset.card_singletonproof · cited by 144
- one_nsmulproof · cited by 63
- Finset.inter_singleton_of_memproof · cited by 8
- Finset.sum_piecewiseproof · cited by 2
- Finset.update_eq_piecewiseproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- affineCombination_mem_affineSpanproof · cited by 12
- affineIndependent_iff_indicator_eq_of_affineCombination_eqproof · cited by 4
- eq_affineCombination_of_mem_affineSpanproof · cited by 4
- mem_affineSpan_iff_eq_weightedVSubOfPoint_vaddproof · cited by 1
- mem_vectorSpan_iff_eq_weightedVSubproof · cited by 1