Theorems · Theorem · group theory
nsmul_injOn_Iio_addOrderOf
∀ {G : Type u_1} [inst : AddMonoid G] {x : G}, Set.InjOn (fun x_1 => x_1 • x) (Set.Iio (addOrderOf x))- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- Set.Iiostatement and proof · cited by 1,166
- Set.InjOnstatement and proof · cited by 543
- addOrderOfstatement · cited by 208
- Function.minimalPeriodproof · cited by 100
- add_left_iterate_apply_zeroproof · cited by 3
- Function.iterate_injOn_Iio_minimalPeriodproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- addOrderOf_le_card_univproof · cited by 1