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Theorems · Theorem · group theory

Function.Injective.isOfFinAddOrder_iff

∀ {G : Type u_1} {H : Type u_2} [inst : AddMonoid G] {x : G} [inst_1 : AddMonoid H] {f : G →+ H},
  Function.Injective ⇑f → (IsOfFinAddOrder (f x) ↔ IsOfFinAddOrder x)
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
2 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidAddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddCommGroup.comap_torsion_of_injective · cited by 1AddCommGroup.comap_torsio…AddUnits.isOfFinAddOrder_val · cited by 0AddUnits.isOfFinAddOrder_…DFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidaddOrderOf · cited by 208addOrderOfIsOfFinAddOrder · cited by 105IsOfFinAddOrderaddOrderOf_pos_iff · cited by 10addOrderOf_pos_iffaddOrderOf_injective · cited by 5addOrderOf_injectiveInjective.isOfFinAddOrder_iffCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.