Theorems · Theorem · commutative algebra
dvd_lcm_left
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] (a b : α), a ∣ lcm a b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- dvd_reflproof · cited by 97
- GCDMonoidstatement and proof · cited by 96
- GCDMonoid.lcmstatement and proof · cited by 78
- lcm_dvd_iffproof · cited by 6
Cited by17
Results whose statement or proof uses this declaration.
- lcm_dvd_lcmproof · cited by 8
- lcm_sameproof · cited by 5
- lcm_assocproof · cited by 2
- dvd_lcm_of_dvd_leftproof · cited by 2
- lcm_commproof · cited by 2
- Monoid.exponent_prodproof · cited by 2
- lcm_mul_leftproof · cited by 2
- AddMonoid.exponent_prodproof · cited by 1
- DihedralGroup.exponentproof · cited by 1
- lcm_eq_left_iffproof · cited by 1
- IsPrimitiveRoot.dvd_of_isCyclotomicExtensionproof · cited by 1
- Ideal.sup_mul_infproof · cited by 1