∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {g : G} {a b : α},
  b = g +ᵥ a → AddSubgroup.map (↑(Additive.toMul (AddAut.conj g))) (AddAction.stabilizer G a) = AddAction.stabilizer G b