-- Lean 4 proof step from Mathlib.RingTheory.LaurentSeries (goal)
Goal:
K : Type u_2
inst : Field K
a : adicCompletion (R := K[X]) K⟮X⟯ (idealX K)
this :
  ∀ (s : Set (adicCompletion (R := K[X]) K⟮X⟯ (idealX K))),
    Membership.mem (γ := Filter (adicCompletion (R := K[X]) K⟮X⟯ (idealX K))) (𝓝 0) s ↔
      ∃ (γ :
        (MonoidWithZeroHom.ValueGroup₀ (F :=
            Valuation (adicCompletion (R := K[X]) K⟮X⟯ (idealX K)) (WithZero (Multiplicative ℤ))) Valued.v)ˣ),
        {x : adicCompletion (R := K[X]) K⟮X⟯ (idealX K) |
            ((Valuation.restrict Valued.v :
                    Valuation (adicCompletion (R := K[X]) K⟮X⟯ (idealX K))
                      (MonoidWithZeroHom.ValueGroup₀ (F :=
                        adicCompletion (R := K[X]) K⟮X⟯ (idealX K) →*₀ WithZero (Multiplicative ℤ))
                        (↑Valued.v : adicCompletion K⟮X⟯ (idealX K) →*₀ WithZero (Multiplicative ℤ)))) :
                  (a : adicCompletion K⟮X⟯ (idealX K)) →
                    MonoidWithZeroHom.ValueGroup₀
                      (↑Valued.v : adicCompletion K⟮X⟯ (idealX K) →*₀ WithZero (Multiplicative ℤ)))
                x <
              (↑γ : MonoidWithZeroHom.ValueGroup₀ Valued.v)} ⊆
          s
ha : ¬a = 0
⊢ Tendsto (α := K⟮X⟯) (β := WithZero (Multiplicative ℤ))
    ((⇑Valued.v : (a : K⟮X⟯) → WithZero (Multiplicative ℤ)) : (a : K⟮X⟯) → WithZero (Multiplicative ℤ))
    (Filter.comap
      (fun (x : K⟮X⟯) ↦
        (↑((RingEquiv.symm (WithVal.equiv (valuation (R := K[X]) K⟮X⟯ (idealX K))) :
                (a : K⟮X⟯) → WithVal (valuation K⟮X⟯ (idealX K)))
              x) :
          UniformSpace.Completion (WithVal (valuation K⟮X⟯ (idealX K)))))
      (𝓝 a))
    (𝓝
        (((Valued.v : Valuation (adicCompletion (R := K[X]) K⟮X⟯ (idealX K)) (WithZero (Multiplicative ℤ))) :
            (a : adicCompletion K⟮X⟯ (idealX K)) → WithZero (Multiplicative ℤ))
          a) :
      Filter (WithZero (Multiplicative ℤ)))
have neg : ∃ (γ :
  (MonoidWithZeroHom.ValueGroup₀ (F :=
      Valuation (adicCompletion (R := K[X]) K⟮X⟯ (idealX K)) (WithZero (Multiplicative ℤ))) Valued.v)ˣ),
  Subset.{u_2} (α := Set (adicCompletion (R := K[X]) K⟮X⟯ (idealX K)))
    {y : adicCompletion (R := K[X]) K⟮X⟯ (idealX K) |
      ((Valuation.restrict Valued.v :
              Valuation (adicCompletion (R := K[X]) K⟮X⟯ (idealX K))
                (MonoidWithZeroHom.ValueGroup₀ (F :=
                  adicCompletion (R := K[X]) K⟮X⟯ (idealX K) →*₀ WithZero (Multiplicative ℤ))
                  (↑Valued.v : adicCompletion K⟮X⟯ (idealX K) →*₀ WithZero (Multiplicative ℤ)))) :
            (a : adicCompletion K⟮X⟯ (idealX K)) →
              MonoidWithZeroHom.ValueGroup₀
                (↑Valued.v : adicCompletion K⟮X⟯ (idealX K) →*₀ WithZero (Multiplicative ℤ)))
          (y - a) <
        (↑γ : MonoidWithZeroHom.ValueGroup₀ Valued.v)}
    {x : adicCompletion (R := K[X]) K⟮X⟯ (idealX K) |
      ∀ (a_1 : K⟮X⟯),
        (↑((RingEquiv.symm (WithVal.equiv (valuation (R := K[X]) K⟮X⟯ (idealX K))) :
                    (a : K⟮X⟯) → WithVal (valuation K⟮X⟯ (idealX K)))
                  a_1) :
              UniformSpace.Completion (WithVal (valuation K⟮X⟯ (idealX K)))) =
            x →
          Eq (α := WithZero (Multiplicative ℤ))
            (((Valued.v : Valuation K⟮X⟯ (WithZero (Multiplicative ℤ))) : (a : K⟮X⟯) → WithZero (Multiplicative ℤ))
                a_1 :
              WithZero (Multiplicative ℤ))
            (((Valued.v : Valuation (adicCompletion (R := K[X]) K⟮X⟯ (idealX K)) (WithZero (Multiplicative ℤ))) :
                  (a : adicCompletion K⟮X⟯ (idealX K)) → WithZero (Multiplicative ℤ))
                a :
              WithZero (Multiplicative ℤ))}
Tactic: rw [WithZeroTopology.tendsto_of_ne_zero ((Valuation.ne_zero_iff Valued.v).mpr ha),
      Filter.eventually_comap, Filter.Eventually, Valued.mem_nhds]