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Theorems · Theorem · combinatorics

Multiset.prod_join

∀ {α : Type u_1} [inst : CommMonoid α] {S : Multiset (Multiset α)}, S.join.prod = (Multiset.map Multiset.prod S).prod
Defined in
Mathlib.Data.Multiset.Bind
Cited by
1 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoid
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Around this declaration

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

Multiset.prod_bind · cited by 0Multiset.prod_bindMultiset · cited by 2627MultisetCommMonoid · cited by 2264CommMonoidMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodMultiset.map_cons · cited by 93Multiset.map_consMultiset.prod_cons · cited by 68Multiset.prod_consMultiset.induction · cited by 31Multiset.inductionMultiset.join · cited by 21Multiset.joinMultiset.prod_add · cited by 18Multiset.prod_addMultiset.join_cons · cited by 9Multiset.join_consMultiset.prod_joinCITED BYCITES

Cites10

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Cited by1

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