Theorems · Theorem · commutative algebra
Commute.pow_dvd_pow_of_sub_pow_eq_zero
∀ {R : Type u_1} {x y : R} {n m p : ℕ} [inst : Ring R], n + m ≤ p + 1 → Commute x y → (x - y) ^ n = 0 → x ^ m ∣ y ^ p- Defined in
- Mathlib.Algebra.Ring.Divisibility.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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.
- Ringstatement and proof · cited by 7,463
- MulZeroClass.mul_zeroproof · cited by 2,091
- Commutestatement and proof · cited by 639
- sub_add_cancelproof · cited by 344
- neg_subproof · cited by 272
- Commute.symmproof · cited by 79
- neg_powproof · cited by 14
- Commute.sub_leftproof · cited by 9
- Commute.pow_dvd_add_pow_of_pow_eq_zero_leftproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Commute.add_pow_dvd_pow_of_pow_eq_zero_rightproof · cited by 1
- Commute.pow_dvd_sub_pow_of_pow_eq_zero_rightproof · cited by 1
- Commute.pow_dvd_pow_of_add_pow_eq_zeroproof · cited by 0