Theorems · Theorem · commutative algebra
Multiset.lcm_singleton
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {a : α}, {a}.lcm = normalize a- Defined in
- Mathlib.Algebra.GCDMonoid.Multiset
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- normalizestatement · cited by 137
- GCDMonoid.lcmproof · cited by 78
- Multiset.lcmstatement · cited by 20
- Multiset.fold_singletonproof · cited by 2
- lcm_one_rightproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Equiv.Perm.IsThreeCycle.orderOfproof · cited by 4
- Equiv.Perm.IsSwap.orderOfproof · cited by 1
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- Finset.lcm_singletonproof · cited by 0