Theorems · Theorem · group theory
Associated.of_pow_associated_of_prime
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {p₁ p₂ : M} {k₁ k₂ : ℕ},
Prime p₁ → Prime p₂ → 0 < k₁ → Associated (p₁ ^ k₁) (p₂ ^ k₂) → Associated p₁ p₂- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.ne'proof · cited by 1,417
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- dvd_pow_selfproof · cited by 24
- Prime.dvd_of_dvd_powproof · cited by 14
- Associated.dvd_iff_dvd_rightproof · cited by 11
- Prime.dvd_prime_iff_associatedproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- eq_of_prime_pow_eqproof · cited by 5
- Associated.of_pow_associated_of_prime'proof · cited by 1