Theorems · Theorem · group theory
dvd_pow_self
∀ {α : Type u_1} [inst : Monoid α] (a : α) {n : ℕ}, n ≠ 0 → a ∣ a ^ n- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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_rflproof · cited by 80
- Dvd.dvd.powproof · cited by 3
Cited by24
Results whose statement or proof uses this declaration.
- PadicInt.appr_specproof · cited by 4
- Valuation.Uniformizer.is_generatorproof · cited by 4
- exists_associated_pow_of_mul_eq_powproof · cited by 3
- Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicityproof · cited by 3
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- Associated.of_pow_associated_of_primeproof · cited by 2
- ZMod.orderOf_one_add_mul_prime_powproof · cited by 2
- NumberField.not_dvd_discr_iff_forall_liesOverproof · cited by 2
- Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvdproof · cited by 2
- Polynomial.cyclotomic_irreducible_pow_of_irreducible_powproof · cited by 2
- IsPGroup.center_nontrivialproof · cited by 2
- Nat.squarefree_pow_iffproof · cited by 2