Theorems · Theorem · commutative algebra
Finset.lcm_dvd_iff
∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
{f : β → α} {a : α}, s.lcm f ∣ a ↔ ∀ b ∈ s, f b ∣ a- Defined in
- Mathlib.Algebra.GCDMonoid.Finset
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 54 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
- Finset.valproof · cited by 438
- NormalizedGCDMonoidstatement and proof · cited by 159
- Finset.lcmstatement · cited by 37
- Multiset.lcm_dvdproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Finset.dvd_lcmproof · cited by 10
- Finset.lcm_dvdproof · cited by 7