Theorems · Theorem · ring theory
Multiset.prod_eq_zero
∀ {M₀ : Type u_3} [inst : CommMonoidWithZero M₀] {s : Multiset M₀}, 0 ∈ s → s.prod = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MulZeroClass.zero_mulproof · cited by 1,625
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodstatement and proof · cited by 528
- Multiset.consproof · cited by 313
- Multiset.prod_consproof · cited by 68
- Multiset.exists_cons_of_memproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.aeval_root_of_mapAlg_eq_multiset_prod_X_sub_Cproof · cited by 2
- Polynomial.isIntegral_coeff_of_factorsproof · cited by 1
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1