Theorems · Theorem · commutative algebra
Multiset.lcm_dvd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Multiset α} {a : α},
s.lcm ∣ a ↔ ∀ b ∈ s, b ∣ a- Defined in
- Mathlib.Algebra.GCDMonoid.Multiset
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 24 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.
- Multisetstatement and proof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- Multiset.induction_onproof · cited by 109
- Multiset.lcmstatement and proof · cited by 20
- Multiset.lcm_consproof · cited by 6
- Multiset.lcm_zeroproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Multiset.dvd_lcmproof · cited by 2
- Finset.lcm_dvd_iffproof · cited by 2
- Equiv.Perm.pow_prime_eq_one_iffproof · cited by 2
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1
- Multiset.lcm_monoproof · cited by 0
- Equiv.Perm.isThreeCycle_sq_of_three_mem_cycleType_fiveproof · cited by 0