Theorems · Theorem · commutative algebra
lcm_eq_of_associated_left
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {m n : α},
Associated m n → ∀ (k : α), lcm m k = lcm n k- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- NormalizedGCDMonoidstatement and proof · cited by 159
- Associated.symmproof · cited by 87
- dvd_rflproof · cited by 80
- GCDMonoid.lcmstatement · cited by 78
- Associated.dvdproof · cited by 38
- dvd_antisymm_of_normalize_eqproof · cited by 15
- lcm_dvd_lcmproof · cited by 8
- normalize_lcmproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.lcm_dedupproof · cited by 3