Theorems · Theorem · group theory
Finset.noncommSum_single
∀ {ι : Type u_2} {M : ι → Type u_6} [inst : (i : ι) → AddMonoid (M i)] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
(x : (i : ι) → M i), Finset.univ.noncommSum (fun i => Pi.single i (x i)) ⋯ = x- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- AddMonoidstatement and proof · cited by 2,864
- add_zeroproof · cited by 2,707
- Finset.cardproof · cited by 2,327
- Pi.singlestatement and proof · cited by 518
- Finset.eraseproof · cited by 455
- Finset.mem_univproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.iSup_map_singleproof · cited by 1
- AddMonoidHom.pi_extproof · cited by 0