∀ (R : Type u_1) {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
  [inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] (x : (PreQuasiregular A)ˣ),
  ↑(↑((Unitization.unitsFstOne_mulEquiv_quasiregular R).symm x))⁻¹ = 1 + ↑(PreQuasiregular.equiv.symm ↑x⁻¹)