Theorems · Theorem · commutative algebra
Multiset.prod_ne_zero_of_prime
∀ {M₀ : Type u_3} [inst : CommMonoidWithZero M₀] [NoZeroDivisors M₀] [Nontrivial M₀] (s : Multiset M₀),
(∀ x ∈ s, Prime x) → s.prod ≠ 0- Defined in
- Mathlib.Algebra.BigOperators.Associated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Primestatement and proof · cited by 277
- Prime.ne_zeroproof · cited by 47
- Multiset.prod_ne_zeroproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_prod_of_primeproof · cited by 2
- UniqueFactorizationMonoid.prod_ne_zero_of_subset_normalizedFactorsproof · cited by 1