Theorems · Theorem · group theory
Finset.noncommProd_mulSingle
∀ {ι : Type u_2} {M : ι → Type u_6} [inst : (i : ι) → Monoid (M i)] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι]
(x : (i : ι) → M i), Finset.univ.noncommProd (fun i => Pi.mulSingle 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
- MonoidFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- Finset.univstatement and proof · cited by 3,473
- Finset.cardproof · cited by 2,327
- one_powproof · cited by 521
- Finset.eraseproof · cited by 455
- Finset.mem_univproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- MonoidHom.pi_extproof · cited by 1
- Submonoid.iSup_map_mulSingleproof · cited by 1