Theorems · Theorem · order theory
pow_eq_pow_iff_of_ne_zero
∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a b : R} {n : ℕ},
n ≠ 0 → (a ^ n = b ^ n ↔ a = b ∨ a = -b ∧ Even n)- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsOrderedRingproof · cited by 777
- Evenstatement and proof · cited by 444
- Oddproof · cited by 364
- abs_nonnegproof · cited by 168
- StrictMono.injectiveproof · cited by 94
- Xorproof · cited by 56
- pow_left_inj₀proof · cited by 7
- Odd.strictMono_powproof · cited by 7
- Even.pow_absproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- zpow_eq_zpow_iff_of_ne_zero₀proof · cited by 1
- pow_eq_one_iff_of_ne_zeroproof · cited by 0