Theorems · Theorem · ring theory
Multiset.prod_map_sum
∀ {R : Type u_4} [inst : CommSemiring R] {s : Multiset (Multiset R)},
(Multiset.map Multiset.sum s).prod = (Multiset.map Multiset.prod s.Sections).sum- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement and proof · cited by 876
- Multiset.prodstatement and proof · cited by 528
- Multiset.sumstatement and proof · cited by 388
- Multiset.consproof · cited by 313
- Multiset.map_congrproof · cited by 232
- Multiset.map_mapproof · cited by 151
- Multiset.induction_onproof · cited by 109
- Multiset.map_consproof · cited by 93
- Multiset.prod_consproof · cited by 68
- Multiset.bindproof · cited by 59
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