Theorems · Theorem · group theory
Finset.sum_insert
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} {a : ι} [inst : AddCommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
a ∉ s → ∑ x ∈ insert a s, f x = f a + ∑ x ∈ s, f x- Cited by
- 196 results in Mathlib
- Foundations
- Depth 55 from the axioms, rests on 847 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.fold_insertproof · cited by 11
Cited by196
Results whose statement or proof uses this declaration.
- sum_applyproof · cited by 83
- MeasureTheory.measure_union_leproof · cited by 43
- Finset.add_sum_eraseproof · cited by 28
- Polynomial.induction_onproof · cited by 23
- Finset.sum_eq_zero_iff_of_nonnegproof · cited by 19
- Finset.sum_range_succ_commproof · cited by 12
- affineIndependent_iff_linearIndependent_vsubproof · cited by 11
- Finset.sum_pairproof · cited by 11
- TensorProduct.tmul_sumproof · cited by 10
- Finset.sum_eq_sum_Ico_succ_botproof · cited by 8
- Finset.prod_addproof · cited by 7
- Affine.Simplex.sum_pointsWithCircumcenterproof · cited by 7