Theorems · Theorem · group theory
IsUnit.orderOf_eq_one
∀ {G : Type u_1} [inst : Monoid G] [Subsingleton Gˣ] {x : G}, IsUnit x → orderOf x = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- IsUnitstatement and proof · cited by 1,602
- orderOfstatement and proof · cited by 324
- orderOf_oneproof · cited by 15
- isUnit_iff_eq_oneproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.