Theorems · Theorem · group theory
pow_inj_iff_of_orderOf_eq_zero
∀ {G : Type u_1} [inst : LeftCancelMonoid G] {x : G}, orderOf x = 0 → ∀ {n m : ℕ}, x ^ n = x ^ m ↔ n = m- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoid
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- orderOfstatement and proof · cited by 324
- Nat.ModEqproof · cited by 225
- LeftCancelMonoidstatement and proof · cited by 28
- Nat.modEq_zero_iffproof · cited by 8
- pow_eq_pow_iff_modEqproof · cited by 5
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