-- Lean 4 proof step from Mathlib.RingTheory.MvPolynomial.Localization (goal)
Goal:
σ : Type u_1
R : Type u_2
inst : CommRing R
M : Submonoid R
S : Type u_3
inst_1 : CommRing S
inst_2 : Algebra R S
r : R
inst_3 : Away r S
g : R →+*
  HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
    (Ideal.span
      {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
            ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
          1}) :=
  RingHom.comp
    (Ideal.Quotient.mk
      (Ideal.span
        {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
              ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
            1}))
    C
⊢ ∃ (b :
    HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
      (Ideal.span
        {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
              ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
            1})),
    HMul.hMul (α :=
        HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
          (Ideal.span
            {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                  ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
                1}))
        ((Ideal.Quotient.mk
                (Ideal.span
                  {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                        ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
                      1}) :
              (a : MvPolynomial Unit R) →
                MvPolynomial Unit R ⧸ Ideal.span {(C : (a : R) → MvPolynomial Unit R) r * X () - 1})
            ((C : (a : R) → MvPolynomial Unit R) r) :
          HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
            (Ideal.span
              {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                    ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
                  1}))
        b =
      1
have h : HMul.hMul (α :=
    HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
      (Ideal.span
        {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
              ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
            1}))
    (β :=
    HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
      (Ideal.span
        {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
              ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
            1}))
    ((Ideal.Quotient.mk
            (Ideal.span
              {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                    ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
                  1}) :
          (a : MvPolynomial Unit R) →
            MvPolynomial Unit R ⧸ Ideal.span {(C : (a : R) → MvPolynomial Unit R) r * X () - 1})
        ((C : (a : R) → MvPolynomial Unit R) r) :
      HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
        (Ideal.span
          {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
              1}))
    ((Ideal.Quotient.mk
            (Ideal.span
              {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                    ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
                  1}) :
          (a : MvPolynomial Unit R) →
            MvPolynomial Unit R ⧸ Ideal.span {(C : (a : R) → MvPolynomial Unit R) r * X () - 1})
        (X ()) :
      HasQuotient.Quotient (MvPolynomial Unit R) (B := Ideal (MvPolynomial Unit R))
        (Ideal.span
          {HMul.hMul (α := MvPolynomial Unit R) (β := MvPolynomial Unit R)
                ((C : (a : R) → MvPolynomial Unit R) r : MvPolynomial Unit R) (X ()) -
              1})) =
  1
Tactic: use (Ideal.Quotient.mk _ <| X ())