letI : Fintype ↑(MulAction.orbit (ConjAct Rˣ) (ConjClasses.exists_rep A|>.choose))
    := by refine Set.fintypeRange fun m => m • Exists.choose ?_
R : Type u_1
inst✝³ : DecidableEq R
inst✝² : DivisionRing R
inst✝¹ : Fintype R
A : ConjClasses Rˣ
inst✝ : Fintype ↑A.carrier
this : Fintype ↑{⋯.choose}.centralizer := Fintype.ofFinite ↑{⋯.choose}.centralizer
⊢ Fintype.card Rˣ = Fintype.card ↑A.carrier * Fintype.card ↑{⋯.choose}.centralizer
R : Type u_1
inst✝³ : DecidableEq R
inst✝² : DivisionRing R
inst✝¹ : Fintype R
A : ConjClasses Rˣ
inst✝ : Fintype ↑A.carrier
this✝ : Fintype ↑{⋯.choose}.centralizer := Fintype.ofFinite ↑{⋯.choose}.centralizer
this : Fintype ↑(MulAction.orbit (ConjAct Rˣ) ⋯.choose) := Set.fintypeRange fun m => m • ⋯.choose
⊢ Fintype.card Rˣ = Fintype.card ↑A.carrier * Fintype.card ↑{⋯.choose}.centralizer