Theorems · Theorem · ring theory
Finsupp.sum_apply
∀ {α : Type u_1} {β : Type u_7} {M : Type u_8} {N : Type u_10} [inst : Zero M] [inst_1 : AddCommMonoid N] {f : α →₀ M}
{g : α → M → β →₀ N} {a₂ : β}, (f.sum g) a₂ = f.sum fun a₁ b => (g a₁ b) a₂- Cited by
- 27 results in Mathlib
- Foundations
- Depth 71 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.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finsupp.supportproof · cited by 828
- Finsupp.sumstatement · cited by 481
- Finsupp.finsetSum_applyproof · cited by 6
Cited by27
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.coeff_mulproof · cited by 13
- MonoidAlgebra.coeff_mulproof · cited by 11
- Finsupp.mapDomain_applyproof · cited by 11
- Finsupp.support_sumproof · cited by 7
- Convexity.StdSimplex.map_constproof · cited by 4
- IsBaseChange.basis_repr_comp_applyproof · cited by 3
- SkewMonoidAlgebra.coeff_sumproof · cited by 3
- Finsupp.mapDomain_apply'proof · cited by 3
- Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smulproof · cited by 3
- TensorProduct.finsuppRight_apply_tmul_applyproof · cited by 3
- TensorProduct.vanishesTrivially_of_sum_tmul_eq_zeroproof · cited by 2
- Finsupp.linearCombination_linearCombinationproof · cited by 2