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Theorems · Theorem · commutative algebra

Multiset.dvd_gcd

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Multiset α} {a : α},
  a ∣ s.gcd ↔ ∀ b ∈ s, a ∣ b
Defined in
Mathlib.Algebra.GCDMonoid.Multiset
Cited by
3 results in Mathlib
Foundations
Depth 24 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.

Finset.dvd_gcd_iff · cited by 9Finset.dvd_gcd_iffMultiset.gcd_dvd · cited by 3Multiset.gcd_dvdMultiset.gcd_mono · cited by 0Multiset.gcd_monoMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidMultiset.induction_on · cited by 109Multiset.induction_onMultiset.gcd · cited by 21Multiset.gcdMultiset.gcd_cons · cited by 7Multiset.gcd_consMultiset.gcd_zero · cited by 6Multiset.gcd_zeroMultiset.dvd_gcdCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.