Theorems · Theorem · commutative algebra
Associates.prod_mk
∀ {M : Type u_2} [inst : CommMonoid M] {p : Multiset M}, (Multiset.map Associates.mk p).prod = Associates.mk p.prod- Defined in
- Mathlib.Algebra.BigOperators.Associated
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- CommMonoidstatement and proof · cited by 2,264
- Multiset.mapstatement and proof · cited by 876
- Multiset.prodstatement and proof · cited by 528
- Associatesstatement · cited by 210
- Associates.mkstatement and proof · cited by 137
- Multiset.induction_onproof · cited by 109
- Multiset.map_consproof · cited by 93
- Multiset.prod_consproof · cited by 68
Cited by6
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- Associates.factors_prodproof · cited by 9
- IsDiscreteValuationRing.associated_pow_irreducibleproof · cited by 4
- Associates.unique'proof · cited by 2
- Associates.finsetProd_mkproof · cited by 1