have := MulAction.card_orbit_mul_card_stabilizer_eq_card_group (ConjAct Rˣ)
    (ConjClasses.exists_rep A|>.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✝¹ : Fintype ↑{⋯.choose}.centralizer := Fintype.ofFinite ↑{⋯.choose}.centralizer
this✝ : Fintype ↑(MulAction.orbit (ConjAct Rˣ) ⋯.choose) := Set.fintypeRange fun m => m • ⋯.choose
this : Fintype ↥(MulAction.stabilizer (ConjAct Rˣ) ⋯.choose) :=
  Fintype.ofFinite ↥(MulAction.stabilizer (ConjAct Rˣ) ⋯.choose)
⊢ 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✝² : Fintype ↑{⋯.choose}.centralizer := Fintype.ofFinite ↑{⋯.choose}.centralizer
this✝¹ : Fintype ↑(MulAction.orbit (ConjAct Rˣ) ⋯.choose) := Set.fintypeRange fun m => m • ⋯.choose
this✝ : Fintype ↥(MulAction.stabilizer (ConjAct Rˣ) ⋯.choose) :=
  Fintype.ofFinite ↥(MulAction.stabilizer (ConjAct Rˣ) ⋯.choose)
this :
  Fintype.card ↑(MulAction.orbit (ConjAct Rˣ) ⋯.choose) * Fintype.card ↥(MulAction.stabilizer (ConjAct Rˣ) ⋯.choose) =
    Fintype.card (ConjAct Rˣ)
⊢ Fintype.card Rˣ = Fintype.card ↑A.carrier * Fintype.card ↑{⋯.choose}.centralizer