Theorems · Theorem · group theory
Dvd.dvd.trans
∀ {α : Type u_1} [inst : Semigroup α] {a b c : α}, a ∣ b → b ∣ c → a ∣ cAlias of dvd_trans.
- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 148 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 15 definitions · uses no axioms
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by148
Results whose statement or proof uses this declaration.
- Nat.minFac_primeproof · cited by 31
- dvd_mul_of_dvd_leftproof · cited by 25
- isUnit_of_dvd_unitproof · cited by 22
- Squarefree.squarefree_of_dvdproof · cited by 15
- Polynomial.le_rootMultiplicity_iffproof · cited by 10
- Nat.Prime.not_coprime_iff_dvdproof · cited by 9
- dvd_gcd_iffproof · cited by 8
- lcm_dvd_lcmproof · cited by 8
- gcd_dvd_gcdproof · cited by 8
- Polynomial.associated_content_mulproof · cited by 6
- dvd_prime_powproof · cited by 6
- Int.ModEq.of_dvdproof · cited by 6