Theorems · Theorem · group theory
Finset.sum_ite_eq
∀ {ι : Type u_1} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : DecidableEq ι] (s : Finset ι) (a : ι) (b : ι → M),
(∑ x ∈ s, if a = x then b x else 0) = if a ∈ s then b a else 0- Cited by
- 85 results in Mathlib
- Foundations
- Depth 71 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.
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.sum_dite_eqproof · cited by 12
Cited by85
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mapproof · cited by 114
- Matrix.mul_adjugateproof · cited by 10
- Matrix.mul_single_apply_sameproof · cited by 7
- AffineBasis.coord_apply_combination_of_memproof · cited by 6
- Matrix.toLinearMap₂'Aux_singleproof · cited by 5
- Matrix.single_mul_apply_sameproof · cited by 4
- Matrix.toLin_conjTransposeproof · cited by 4
- Polynomial.taylor_coeffproof · cited by 4
- Finset.convexHull_eqproof · cited by 4
- LieAlgebra.Basis.baseSupp_apply_h'proof · cited by 3
- Algebra.Generators.map_toComp_kerproof · cited by 3
- linearIndepOn_isGroupLikeElemproof · cited by 3