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Theorems · Theorem · commutative algebra

Finset.lcm_eq_zero_iff

∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
  {f : β → α} [Nontrivial α], s.lcm f = 0 ↔ ∃ x ∈ s, f x = 0
Defined in
Mathlib.Algebra.GCDMonoid.Finset
Cited by
2 results in Mathlib
Foundations
Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizedGCDMonoidNontrivial
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddMonoid.ExponentExists.of_finite · cited by 2ExponentExists.of_finiteIsOfFinAddOrder.pi · cited by 0IsOfFinAddOrder.piFinset · cited by 13712FinsetNontrivial · cited by 2416NontrivialCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.map · cited by 876Multiset.mapFinset.val · cited by 438Finset.valNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidFinset.lcm · cited by 37Finset.lcmFinset.lcm_eq_zero_iffCITED BYCITES

Cites7

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Cited by2

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