Theorems · Theorem · group theory
pow_ne_zero_iff
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {a : M₀} {n : ℕ} [IsReduced M₀], n ≠ 0 → (a ^ n ≠ 0 ↔ a ≠ 0)- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- MonoidWithZeroIsReduced
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Iff.notproof · cited by 489
- MonoidWithZerostatement and proof · cited by 456
- IsReducedstatement and proof · cited by 98
- pow_eq_zero_iffproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- pow_pos_iffproof · cited by 1
- NumberField.det_of_basisMatrix_non_zeroproof · cited by 1
- Even.pow_pos_iffproof · cited by 1
- IsReduced.pow_ne_zero_iffproof · cited by 0