Theorems · Theorem · group theory
pow_inj_mod
∀ {G : Type u_1} [inst : LeftCancelMonoid G] {x : G} {n m : ℕ}, x ^ n = x ^ m ↔ n % orderOf x = m % orderOf x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoid
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.
- orderOfstatement · cited by 324
- LeftCancelMonoidstatement and proof · cited by 28
- pow_eq_pow_iff_modEqproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.nodup_toListproof · cited by 5