Theorems · Theorem · group theory
RightCancelMonoid.injective_pow_iff_not_isOfFinOrder
∀ {G : Type u_1} [inst : RightCancelMonoid G] {x : G}, (Function.Injective fun n => x ^ n) ↔ ¬IsOfFinOrder x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RightCancelMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.ModEqproof · cited by 225
- IsOfFinOrderstatement and proof · cited by 113
- RightCancelMonoidstatement and proof · cited by 18
- Nat.modEq_zero_iffproof · cited by 8
- orderOf_eq_zero_iffproof · cited by 8
- RightCancelMonoid.pow_eq_pow_iff_modEqproof · cited by 3
- not_isOfFinOrder_of_injective_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- RightCancelMonoid.infinite_not_isOfFinOrderproof · cited by 0