Theorems · Theorem · commutative algebra
Finset.lcm_dvd_prod
∀ {ι : Type u_1} {α : Type u_2} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (s : Finset ι)
(f : ι → α), s.lcm f ∣ s.prod f- Defined in
- Mathlib.Algebra.GCDMonoid.FinsetLemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Finset.prodstatement · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- Finset.lcmstatement · cited by 37
- Finset.dvd_prod_of_memproof · cited by 23
- Finset.lcm_dvdproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Finset.associated_lcm_prodproof · cited by 1
- Finset.Rat.den_sum_dvd_prod_denproof · cited by 0