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Theorems · Theorem · group theory

isOfFinOrder_iff_isUnit

∀ {G : Type u_1} [inst : Monoid G] [Finite Gˣ] {x : G}, IsOfFinOrder x ↔ IsUnit x
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
1 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidFinite
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Around this declaration

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

IsUnit.isOfFinOrder · cited by 0IsUnit.isOfFinOrderMonoid · cited by 3887MonoidFinite · cited by 3029FiniteUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valIsUnit · cited by 1602IsUnitIsOfFinOrder · cited by 113IsOfFinOrderisOfFinOrder_of_finite · cited by 14isOfFinOrder_of_finiteIsOfFinOrder.isUnit · cited by 2IsOfFinOrder.isUnitUnits.isOfFinOrder_val · cited by 1Units.isOfFinOrder_valisOfFinOrder_iff_isUnitCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.