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Theorems · Theorem · group theory

Multiset.prod_filter_mul_prod_filter_not

∀ {M : Type u_5} [inst : CommMonoid M] {s : Multiset M} (p : M → Prop) [inst_1 : DecidablePred p],
  (Multiset.filter p s).prod * (Multiset.filter (fun a => ¬p a) s).prod = s.prod
Defined in
Mathlib.Algebra.BigOperators.Group.Multiset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidDecidablePred
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Around this declaration

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Submonoid.LocalizationMap.uniqueFactorizationMonoid · cited by 1LocalizationMap.uniqueFac…Multiset · cited by 2627MultisetCommMonoid · cited by 2264CommMonoidMultiset.prod · cited by 528Multiset.prodMultiset.filter · cited by 102Multiset.filterMultiset.prod_add · cited by 18Multiset.prod_addMultiset.filter_add_not · cited by 4Multiset.filter_add_notMultiset.prod_filter_mul_prod…CITED BYCITES

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