Theorems · Theorem · ring theory
Multiset.prod_ne_zero
∀ {M₀ : Type u_3} [inst : CommMonoidWithZero M₀] [NoZeroDivisors M₀] [Nontrivial M₀] {s : Multiset M₀},
0 ∉ s → s.prod ≠ 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Nontrivialstatement and proof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- NoZeroDivisorsstatement and proof · cited by 545
- Multiset.prodstatement · cited by 528
- Multiset.prod_eq_zero_iffproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_ne_zeroproof · cited by 5
- Multiset.prod_ne_zero_of_primeproof · cited by 2
- UniqueFactorizationMonoid.normalizedFactors_prod_eqproof · cited by 0
- UniqueFactorizationMonoid.normalizedFactors_multiset_prodproof · cited by 0