Theorems · Theorem · commutative algebra
Commute.pow_dvd_pow_of_add_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
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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- Ringstatement and proof · cited by 7,463
- neg_negproof · cited by 960
- Commutestatement and proof · cited by 639
- sub_neg_eq_addproof · cited by 264
- dvd_mul_of_dvd_leftproof · cited by 25
- Commute.neg_rightproof · cited by 7
- neg_pow'proof · cited by 3
- Commute.pow_dvd_pow_of_sub_pow_eq_zeroproof · cited by 3
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