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Theorems · Theorem · group theory

Multiset.prod_map_inv

∀ {ι : Type u_2} {G : Type u_4} [inst : DivisionCommMonoid G] {m : Multiset ι} {f : ι → G},
  (Multiset.map (fun i => (f i)⁻¹) m).prod = (Multiset.map f m).prod⁻¹
Defined in
Mathlib.Algebra.BigOperators.Group.Multiset.Basic
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
DivisionCommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.prod_inv_distrib · cited by 13Finset.prod_inv_distribIsMulFreimanHom.inv · cited by 0IsMulFreimanHom.invMultiset · cited by 2627MultisetMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodMultiset.map_map · cited by 151Multiset.map_mapDivisionCommMonoid · cited by 80DivisionCommMonoidMultiset.prod_map_inv' · cited by 1Multiset.prod_map_inv'Multiset.prod_map_invCITED BYCITES

Cites6

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Cited by2

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