Theorems · Theorem · group theory
pow_dvd_pow_of_dvd
∀ {α : Type u_1} [inst : CommMonoid α] {a b : α}, a ∣ b → ∀ (n : ℕ), a ^ n ∣ b ^ n- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- pow_zeroproof · cited by 1,094
- pow_succproof · cited by 374
- mul_dvd_mulproof · cited by 24
Cited by12
Results whose statement or proof uses this declaration.
- pow_dvd_pow_of_dvd_of_leproof · cited by 3
- emultiplicity_le_emultiplicity_of_dvd_leftproof · cited by 2
- IsIntegrallyClosed.pow_dvd_pow_iffproof · cited by 2
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- IsPGroup.monoproof · cited by 1
- gcd_pow_left_dvd_pow_gcdproof · cited by 1
- gcd_pow_right_dvd_pow_gcdproof · cited by 1
- Polynomial.aeval_pow_two_pow_dvd_aeval_iterate_newtonMapproof · cited by 1
- card_dvd_exponent_pow_rank'proof · cited by 1
- UniqueFactorizationMonoid.pow_dvd_pow_iff_dvdproof · cited by 0
- LindemannWeierstrass.exp_polynomial_approxproof · cited by 0
- card_dvd_exponent_nsmul_rank'proof · cited by 0