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Theorems · Theorem · commutative algebra

Multiset.lcm_eq_zero_iff

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] [Nontrivial α] (s : Multiset α),
  s.lcm = 0 ↔ 0 ∈ s
Defined in
Mathlib.Algebra.GCDMonoid.Multiset
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizedGCDMonoidNontrivial
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Around this declaration

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Multiset.lcm_ne_zero_iff · cited by 0Multiset.lcm_ne_zero_iffMultiset · cited by 2627MultisetNontrivial · cited by 2416NontrivialCommMonoidWithZero · cited by 913CommMonoidWithZeroNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidMultiset.induction_on · cited by 109Multiset.induction_onMultiset.lcm · cited by 20Multiset.lcmMultiset.lcm_cons · cited by 6Multiset.lcm_consMultiset.lcm_zero · cited by 5Multiset.lcm_zeroMultiset.lcm_eq_zero_iffCITED BYCITES

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Cited by1

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