Theorems · Theorem · commutative algebra
Finset.lcm_dvd
∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
{f : β → α} {a : α}, (∀ b ∈ s, f b ∣ a) → s.lcm f ∣ a- 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.
Cites5
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
- Finset.lcmstatement · cited by 37
- Finset.lcm_dvd_iffproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Finset.lcm_dvd_prodproof · cited by 2
- Monoid.lcm_orderOf_dvd_exponentproof · cited by 1
- AddMonoid.lcm_addOrderOf_dvd_exponentproof · cited by 1
- Monoid.exponent_piproof · cited by 0
- AddMonoid.exponent_piproof · cited by 0
- Finset.lcm_monoproof · cited by 0
- Finset.lcm_mono_funproof · cited by 0