Theorems · Theorem · commutative algebra
exists_associated_mem_of_dvd_prod
∀ {M₀ : Type u_3} [inst : CommMonoidWithZero M₀] [IsCancelMulZero M₀] {p : M₀},
Prime p → ∀ {s : Multiset M₀}, (∀ r ∈ s, Prime r) → p ∣ s.prod → ∃ q ∈ s, Associated p q- Defined in
- Mathlib.Algebra.BigOperators.Associated
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodstatement and proof · cited by 528
- Multiset.consproof · cited by 313
- Associatedstatement and proof · cited by 296
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- Multiset.induction_onproof · cited by 109
- Multiset.prod_consproof · cited by 68
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_consproof · cited by 29
- Prime.not_isUnitproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- prime_factors_uniqueproof · cited by 3