Theorems · Theorem · group theory
Multiset.prod_map_zpow
∀ {ι : Type u_2} {G : Type u_4} [inst : DivisionCommMonoid G] {m : Multiset ι} {f : ι → G} {n : ℤ},
(Multiset.map (fun i => f i ^ n) m).prod = (Multiset.map f m).prod ^ n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Multisetstatement and proof · cited by 2,627
- CommMonoidproof · cited by 2,264
- Multiset.mapstatement and proof · cited by 876
- Multiset.prodstatement and proof · cited by 528
- Multiset.map_congrproof · cited by 232
- Multiset.map_mapproof · cited by 151
- DivisionCommMonoidstatement and proof · cited by 80
- zpowGroupHomproof · cited by 12
- Multiset.prod_homproof · cited by 8
- zpowGroupHom_applyproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Finset.prod_zpowproof · cited by 0