Theorems · Theorem · ring theory
Finsupp.univ_sum_single
∀ {α : Type u_1} {M : Type u_8} [inst : Fintype α] [inst_1 : AddCommMonoid M] (f : α →₀ M), (∑ a, fun₀ | a => f a) = fThe Finsupp version of Finset.univ_sum_single
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Fintypestatement and proof · cited by 7,736
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Finsupp.singlestatement and proof · cited by 943
- DFunLike.coe_injectiveproof · cited by 161
- Finsupp.single_eq_pi_singleproof · cited by 15
- Finsupp.coe_finsetSumproof · cited by 15
- Finset.univ_sum_singleproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- FunOnFinite.map_apply_applyproof · cited by 2
- Finsupp.equivFunOnFinite_symm_eq_sumproof · cited by 2
- Module.Flat.tfae_equational_criterionproof · cited by 2
- Pi.counit_comp_finsuppLcoeFunproof · cited by 1
- Pi.comul_comp_finsuppLcoeFunproof · cited by 1
- LinearMap.trace_smulRightproof · cited by 0