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Theorems · Theorem · commutative algebra

Finset.gcd_cons

∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
  {f : β → α} {b : β} (h : b ∉ s), (Finset.cons b s h).gcd f = gcd (f b) (s.gcd f)
Defined in
Mathlib.Algebra.GCDMonoid.Finset
Cited by
1 results in Mathlib
Foundations
Depth 58 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.Int.finsetGcd_nonneg · cited by 0Int.finsetGcd_nonnegFinset · cited by 13712FinsetCommMonoidWithZero · cited by 913CommMonoidWithZeroFinset.cons · cited by 221Finset.consNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidGCDMonoid.gcd · cited by 143GCDMonoid.gcdFinset.gcd · cited by 49Finset.gcdFinset.fold_cons · cited by 6Finset.fold_consFinset.gcd_consCITED BYCITES

Cites7

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Cited by1

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