Theorems · Theorem · commutative algebra
Finset.lcm_insert
∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
{f : β → α} [inst_2 : DecidableEq β] {b : β}, (insert b s).lcm f = lcm (f b) (s.lcm f)- Defined in
- Mathlib.Algebra.GCDMonoid.Finset
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.lcmstatement and proof · cited by 78
- Finset.lcmstatement and proof · cited by 37
- Finset.insert_eq_of_memproof · cited by 28
- Finset.fold_insertproof · cited by 11
- Finset.dvd_lcmproof · cited by 10
- Multiset.normalize_lcmproof · cited by 2
- lcm_eq_right_iffproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- ArithmeticFunction.carmichael_finset_lcmproof · cited by 1
- Finset.Rat.den_sum_dvd_lcm_denproof · cited by 1
- Finset.lcm_imageproof · cited by 1
- Finset.factorization_lcmproof · cited by 1
- Finset.lcm_unionproof · cited by 0