Theorems · Theorem · ring theory
Finsupp.sum_fun_zero
∀ {α : Type u_1} {M : Type u_8} {N : Type u_10} [inst : Zero M] [inst_1 : AddCommMonoid N] (f : α →₀ M),
(f.sum fun x x_1 => 0) = 0- Cited by
- 29 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finset.sum_congrproof · cited by 2,323
- Finsupp.supportproof · cited by 828
- Finsupp.sumstatement · cited by 481
- Finset.sum_const_zeroproof · cited by 219
Cited by29
Results whose statement or proof uses this declaration.
- Polynomial.X_mulproof · cited by 12
- MvPolynomial.coeff_C_mulproof · cited by 9
- LinearMap.toMatrix₂_compl₁₂proof · cited by 7
- LinearMap.toMatrix₂'_compl₁₂proof · cited by 6
- Matrix.PosDef.posSemidefproof · cited by 5
- Convexity.StdSimplex.map_constproof · cited by 4
- MonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 4
- AddMonoidAlgebra.coeff_single_mul_eq_mul_coeffproof · cited by 3
- AddMonoidAlgebra.coeff_single_mul_of_forall_add_neproof · cited by 3
- Matrix.PosSemidef.submatrixproof · cited by 3
- Matrix.PosDef.transposeproof · cited by 2
- AddMonoidAlgebra.coeff_mul_single_of_forall_add_neproof · cited by 2