Theorems · Theorem · group theory
pow_ne_zero
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {a : M₀} [IsReduced M₀] (n : ℕ), a ≠ 0 → a ^ n ≠ 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 208 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 51 definitions · uses no axioms
- Assumes
- MonoidWithZeroIsReduced
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidWithZerostatement and proof · cited by 456
- IsReducedstatement and proof · cited by 98
- eq_zero_of_pow_eq_zeroproof · cited by 30
Cited by208
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_eq_int_iffproof · cited by 31
- zpow_ne_zeroproof · cited by 30
- Real.log_powproof · cited by 29
- meromorphicOrderAt_eq_top_iffproof · cited by 20
- Nat.ordProj_dvdproof · cited by 17
- Nat.factorization_powproof · cited by 17
- map_wittStructureIntproof · cited by 13
- Polynomial.natDegree_powproof · cited by 11
- ENNReal.inv_powproof · cited by 9
- MeromorphicAt.invproof · cited by 9
- pow_sub₀proof · cited by 9
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
Showing the 200 most cited of 208.