Theorems · Theorem · group theory
injective_nsmul_iff_not_isOfFinAddOrder
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] {x : G}, (Function.Injective fun n => n • x) ↔ ¬IsOfFinAddOrder 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
- AddLeftCancelMonoid
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
- IsOfFinAddOrderstatement and proof · cited by 105
- AddLeftCancelMonoidstatement and proof · cited by 37
- addOrderOf_eq_zero_iffproof · cited by 9
- Nat.modEq_zero_iffproof · cited by 8
- nsmul_eq_nsmul_iff_modEqproof · cited by 4
- not_isOfFinAddOrder_of_injective_nsmulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- infinite_not_isOfFinAddOrderproof · cited by 2