Theorems · Theorem · group theory
Multiset.prod_cons
∀ {M : Type u_3} [inst : CommMonoid M] (a : M) (s : Multiset M), (a ::ₘ s).prod = a * s.prod- Cited by
- 68 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Multiset.consstatement · cited by 313
- Multiset.foldr_consproof · cited by 4
Cited by68
Results whose statement or proof uses this declaration.
- Multiset.prod_singletonproof · cited by 29
- Polynomial.Splits.exists_eval_eq_zeroproof · cited by 14
- UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvdproof · cited by 8
- Equiv.Perm.sign_of_cycleTypeproof · cited by 7
- Polynomial.monic_multiset_prod_of_monicproof · cited by 6
- Associates.prod_mkproof · cited by 6
- WfDvdMonoid.exists_factorsproof · cited by 5
- UniqueFactorizationMonoid.exists_mem_factors_of_dvdproof · cited by 4
- Multiset.prod_eq_zeroproof · cited by 4
- Polynomial.natDegree_multiset_prod'proof · cited by 3
- Ideal.IsPrime.multiset_prod_leproof · cited by 3
- Polynomial.Monic.nextCoeff_multiset_prodproof · cited by 3