Theorems · Theorem · commutative algebra
Finset.gcd_dvd
∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
{f : β → α} {b : β}, b ∈ s → s.gcd f ∣ f b- Defined in
- Mathlib.Algebra.GCDMonoid.Finset
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- dvd_rflproof · cited by 80
- Finset.gcdstatement · cited by 49
- Finset.dvd_gcd_iffproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- Finset.gcd_insertproof · cited by 9
- Polynomial.content_dvd_coeffproof · cited by 3
- IsGCDMonoid.isPrincipal_of_exists_mul_ne_zero_isPrincipalproof · cited by 1
- Finset.extract_gcdproof · cited by 1
- Finset.gcd_monoproof · cited by 1
- Finset.gcd_mono_funproof · cited by 0
- fermatLastTheoremWith_of_fermatLastTheoremWith_coprimeproof · cited by 0