Theorems · Theorem · commutative algebra
Finset.associated_lcm_prod
∀ {ι : Type u_1} {α : Type u_2} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset ι}
{f : ι → α}, (↑s).Pairwise (Function.onFun IsRelPrime f) → Associated (s.lcm f) (s.prod f)- Defined in
- Mathlib.Algebra.GCDMonoid.FinsetLemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- SetLike.coestatement and proof · cited by 8,199
- Finset.prodstatement · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Function.onFunstatement and proof · cited by 570
- Set.Pairwisestatement and proof · cited by 321
- Associatedstatement · cited by 296
- NormalizedGCDMonoidstatement and proof · cited by 159
- IsRelPrimestatement and proof · cited by 136
- Finset.lcmstatement · cited by 37
- associated_of_dvd_dvdproof · cited by 28
- Finset.dvd_lcmproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Finset.lcm_eq_prodproof · cited by 1