Theorems · Theorem · group theory
Multiset.prod_add
∀ {M : Type u_5} [inst : CommMonoid M] (s t : Multiset M), (s + t).prod = s.prod * t.prod- Cited by
- 18 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.prodstatement · cited by 528
Cited by18
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- Multiset.prod_dvd_prod_of_leproof · cited by 9
- Ideal.eq_prime_pow_mul_coprimeproof · cited by 3
- PrimeMultiset.prod_addproof · cited by 3
- Equiv.Perm.sign_of_cycleType'proof · cited by 2
- Associates.prod_le_prodproof · cited by 2
- Associates.prod_addproof · cited by 2
- UniqueFactorizationMonoid.factors_mulproof · cited by 1
- Multiset.prod_filter_mul_prod_filter_notproof · cited by 1
- irreducible_iff_prime_of_existsUnique_irreducible_factorsproof · cited by 1
- WfDvdMonoid.of_exists_prime_factorsproof · cited by 1
- Multiset.prod_joinproof · cited by 1