Theorems · Theorem · group theory
Finset.univ_sum_single
∀ {I : Type u_7} [inst : DecidableEq I] {M : I → Type u_8} [inst_1 : (i : I) → AddCommMonoid (M i)] [inst_2 : Fintype I]
(f : (i : I) → M i), ∑ i, Pi.single i (f i) = f- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Pi.singlestatement and proof · cited by 518
- Finset.mem_univproof · cited by 361
- Finset.sum_applyproof · cited by 234
- Finset.sum_pi_singleproof · cited by 8
Cited by11
Results whose statement or proof uses this declaration.
- Finsupp.univ_sum_singleproof · cited by 6
- AddMonoidHom.functions_extproof · cited by 3
- IsModuleTopology.continuous_bilinear_of_pi_fintypeproof · cited by 1
- AlgHom.eq_piEvalAlgHomproof · cited by 1
- Algebra.FormallyUnramified.pi_iffproof · cited by 1
- CompleteOrthogonalIdempotents.singleproof · cited by 1
- Submodule.iSup_map_singleproof · cited by 1
- LinearMap.lsum_singleproof · cited by 1
- parallelepiped_singleproof · cited by 1
- Pi.single_inductionproof · cited by 1
- MultilinearMap.pi_extproof · cited by 1