Theorems · Definition · group theory
Units.ofPow
{M : Type u_1} → [inst : Monoid M] → (u : Mˣ) → (x : M) → {n : ℕ} → n ≠ 0 → x ^ n = ↑u → MˣIf a natural power of x is a unit, then x is a unit.
- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Units.leftOfMulproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- isUnit_pow_iffproof · cited by 7
- Units.ofPowEqOneproof · cited by 6