Mathlib Map

Theorems · Theorem · group theory

dvd_rfl

∀ {α : Type u_1} [inst : Monoid α] {a : α}, a ∣ a
Defined in
Mathlib.Algebra.Divisibility.Basic
Cited by
80 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CharP.cast_eq_zero · cited by 357CharP.cast_eq_zeroPrime.irreducible · cited by 54Prime.irreducibledvd_pow_self · cited by 24dvd_pow_selfNat.dvd_prime · cited by 18Nat.dvd_primeWfDvdMonoid.exists_irreducible_factor · cited by 12WfDvdMonoid.exists_irredu…FiniteField.card · cited by 10FiniteField.cardFinset.dvd_lcm · cited by 10Finset.dvd_lcmEuclideanDomain.gcd_dvd · cited by 8EuclideanDomain.gcd_dvdFinset.gcd_dvd · cited by 7Finset.gcd_dvdNat.mem_divisors_self · cited by 6Nat.mem_divisors_selflcm_same · cited by 5lcm_sameZMod.algebra · cited by 5ZMod.algebraIrreducible.isRelPrime_iff_not_dvd · cited by 4Irreducible.isRelPrime_if…Int.associated_natAbs · cited by 4Int.associated_natAbseq_of_forall_dvd · cited by 4eq_of_forall_dvdMonoid · cited by 3887Monoiddvd_refl · cited by 97dvd_refldvd_rflCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Monoidstatement and proof · cited by 3,887
  • dvd_reflproof · cited by 97

Cited by82

Results whose statement or proof uses this declaration.