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Theorems · Theorem · group theory

Multiset.prod_map_div

∀ {ι : Type u_2} {G : Type u_4} [inst : DivisionCommMonoid G] {m : Multiset ι} {f g : ι → G},
  (Multiset.map (fun i => f i / g i) m).prod = (Multiset.map f m).prod / (Multiset.map g m).prod
Defined in
Mathlib.Algebra.BigOperators.Group.Multiset.Basic
Cited by
2 results in Mathlib
Foundations
Depth 14 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_div_distrib · cited by 9Finset.prod_div_distribIsMulFreimanHom.div · cited by 0IsMulFreimanHom.divMultiset · cited by 2627MultisetMultiset.map · cited by 876Multiset.mapdiv_one · cited by 629div_oneMultiset.prod · cited by 528Multiset.prodDivisionCommMonoid · cited by 80DivisionCommMonoidmul_div_mul_comm · cited by 11mul_div_mul_commMultiset.prod_hom₂ · cited by 2Multiset.prod_hom₂Multiset.prod_map_divCITED BYCITES

Cites7

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Cited by2

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