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Theorems · Theorem · group theory

Multiset.prod_map_pow

∀ {ι : Type u_2} {M : Type u_5} [inst : CommMonoid M] {m : Multiset ι} {f : ι → M} {n : ℕ},
  (Multiset.map (fun i => f i ^ n) m).prod = (Multiset.map f m).prod ^ n
Defined in
Mathlib.Algebra.BigOperators.Group.Multiset.Basic
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
CommMonoid
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Around this declaration

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

Finset.prod_pow · cited by 10Finset.prod_powHeight.mulHeight_eval_le · cited by 3Height.mulHeight_eval_leMultiset · cited by 2627MultisetCommMonoid · cited by 2264CommMonoidMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodpowMonoidHom · cited by 35powMonoidHomMultiset.prod_hom' · cited by 4Multiset.prod_hom'Multiset.prod_map_powCITED BYCITES

Cites6

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Cited by2

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