Theorems · Theorem · commutative algebra
lcm_same
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a : α), lcm a a = normalize a- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 20 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.
- CommMonoidWithZerostatement and proof · cited by 913
- NormalizedGCDMonoidstatement and proof · cited by 159
- normalizestatement · cited by 137
- dvd_rflproof · cited by 80
- GCDMonoid.lcmstatement · cited by 78
- dvd_lcm_leftproof · cited by 17
- lcm_dvdproof · cited by 14
- lcm_eq_normalizeproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Multiset.lcm_addproof · cited by 3
- Multiset.lcm_dedupproof · cited by 3
- lcm_mul_leftproof · cited by 2
- DihedralGroup.not_isCyclicproof · cited by 1
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1