Theorems · Theorem · group theory
not_isOfFinOrder_of_injective_pow
∀ {G : Type u_1} [inst : Monoid G] {x : G}, (Function.Injective fun n => x ^ n) → ¬IsOfFinOrder xSee also injective_pow_iff_not_isOfFinOrder.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- 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
- pow_zeroproof · cited by 1,094
- IsOfFinOrderstatement · cited by 113
- irreflproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- RightCancelMonoid.injective_pow_iff_not_isOfFinOrderproof · cited by 1
- injective_pow_iff_not_isOfFinOrderproof · cited by 1