Theorems · Theorem · group theory
eq_of_prime_pow_eq
∀ {R : Type u_2} [inst : CommMonoidWithZero R] [IsCancelMulZero R] [Subsingleton Rˣ] {p₁ p₂ : R} {k₁ k₂ : ℕ},
Prime p₁ → Prime p₂ → 0 < k₁ → p₁ ^ k₁ = p₂ ^ k₂ → p₁ = p₂- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- associated_iff_eqproof · cited by 28
- Associated.of_pow_associated_of_primeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.discr_prime_powproof · cited by 3
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_twoproof · cited by 2
- IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_twoproof · cited by 1
- AddCommMonoid.primaryComponent.disjointproof · cited by 0
- CommMonoid.primaryComponent.disjointproof · cited by 0