Theorems · Theorem · commutative algebra
Associates.exists_mem_multiset_le_of_prime
∀ {M₀ : Type u_3} [inst : CommMonoidWithZero M₀] {s : Multiset (Associates M₀)} {p : Associates M₀},
Prime p → p ≤ s.prod → ∃ a ∈ s, p ≤ a- Defined in
- Mathlib.Algebra.BigOperators.Associated
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
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Cites13
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
- Primestatement and proof · cited by 277
- Associatesstatement and proof · cited by 210
- Multiset.induction_onproof · cited by 109
- Multiset.prod_consproof · cited by 68
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_cons_of_memproof · cited by 35
- mul_eq_oneproof · cited by 6
- Associates.Prime.le_or_leproof · cited by 1
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