Theorems · Theorem · commutative algebra
dvd_lcm_of_dvd_right
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] {a b : α}, a ∣ b → ∀ (c : α), a ∣ lcm c b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 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.dvd.transproof · cited by 148
- GCDMonoidstatement and proof · cited by 96
- GCDMonoid.lcmstatement · cited by 78
- dvd_lcm_rightproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- Prime.dvd_lcmproof · cited by 1
- Dvd.dvd.lcm_leftproof · cited by 0