Theorems · Theorem · group theory
Function.Injective.isOfFinOrder_iff
∀ {G : Type u_1} {H : Type u_2} [inst : Monoid G] {x : G} [inst_1 : Monoid H] {f : G →* H},
Function.Injective ⇑f → (IsOfFinOrder (f x) ↔ IsOfFinOrder x)- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- orderOfproof · cited by 324
- IsOfFinOrderstatement and proof · cited by 113
- orderOf_injectiveproof · cited by 12
- orderOf_pos_iffproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Units.isOfFinOrder_valproof · cited by 1
- CommGroup.comap_torsion_of_injectiveproof · cited by 1