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Theorems · Theorem · commutative algebra

Multiset.gcd_dvd

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Multiset α} {a : α},
  a ∈ s → s.gcd ∣ a
Defined in
Mathlib.Algebra.GCDMonoid.Multiset
Cited by
3 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizedGCDMonoid
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Around this declaration

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

Multiset.gcd_eq_zero_iff · cited by 2Multiset.gcd_eq_zero_iffMultiset.gcd_mono · cited by 0Multiset.gcd_monoMultiset.extract_gcd · cited by 0Multiset.extract_gcdMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroNormalizedGCDMonoid · cited by 159NormalizedGCDMonoiddvd_rfl · cited by 80dvd_rflMultiset.gcd · cited by 21Multiset.gcdMultiset.dvd_gcd · cited by 3Multiset.dvd_gcdMultiset.gcd_dvdCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.