Theorems · Theorem · group theory
dvd_trans
∀ {α : Type u_1} [inst : Semigroup α] {a b c : α}, a ∣ b → b ∣ c → a ∣ c- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 6 from the axioms · 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 by50
Results whose statement or proof uses this declaration.
- Dvd.dvd.transproof · cited by 148
- UniqueFactorizationMonoid.dvd_of_mem_normalizedFactorsproof · cited by 20
- WfDvdMonoid.exists_irreducible_factorproof · cited by 12
- Prime.dvd_finsetProd_iffproof · cited by 7
- Units.mul_right_dvdproof · cited by 7
- Nat.coprime_of_dvdproof · cited by 7
- DirichletCharacter.changeLevel_transstatement and proof · cited by 6
- Ideal.span_singleton_dvd_span_singleton_iff_dvdproof · cited by 6
- UniqueFactorizationMonoid.dvd_of_mem_factorsproof · cited by 5
- Polynomial.C_mul_dvdproof · cited by 4
- exists_bijective_map_powersproof · cited by 3
- ZMod.unitsMap_compstatement and proof · cited by 2