-- Module: Mathlib.Topology.Category.Stonean.Basic
Goal:
X Y : Stonean
f : X ⟶ Y
h : Epi f
y : (↑(Y.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)
hy :
  ∀ (a : (↑(X.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)),
    (ConcreteCategory.hom (FC :=
            fun (x1 x2 : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
            C((↑(x1.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1),
              (↑(x2.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)))
            (CC := fun (X : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
            (↑(X.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)) f :
          (a : (↑X.toTop : Type u_1)) → (↑Y.toTop : Type u_1))
        a ≠
      y
C : Set
  ((fun (X : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
      (↑(X.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1))
    Y) :=
  Set.range (ι :=
    (fun (X : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
        (↑(X.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1))
      X)
    (⇑(ConcreteCategory.hom (FC :=
          fun (x1 x2 : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
          C((↑(x1.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1),
            (↑(x2.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)))
          (CC := fun (X : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
          (↑(X.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)) f) :
      (a :
          (fun (X : CompHausLike fun (X : TopCat) ↦ ExtremallyDisconnected (↑X : Type u_1)) ↦ (↑X.toTop : Type u_1))
            X) →
        (fun (X : CompHausLike fun (X : TopCat) ↦ ExtremallyDisconnected (↑X : Type u_1)) ↦ (↑X.toTop : Type u_1)) Y)
hC : IsClosed C
U : Set
  ((fun (X : CompHausLike fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1)) ↦
      (↑(X.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1))
    Y) :=
  Cᶜ
hUy : U ∈ 𝓝 y
obtain :
  ∀ (V : Set (↑(Y.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1))
    (hV :
      Membership.mem (γ :=
        Set (Set (↑(Y.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1)))
        {s : Set (↑(Y.toTop (P := fun (X : TopCat.{u_1}) ↦ ExtremallyDisconnected.{u_1} (↑X : Type u_1))) : Type u_1) |
          IsClopen s}
        V)
    (hyV : y ∈ V) (hVU : V ⊆ U), False
⊢ False

Tactic:
obtain ⟨V, hV, hyV, hVU⟩ := isTopologicalBasis_isClopen.mem_nhds_iff.mp hUy

Premises used: isTopologicalBasis_isClopen, Iff.mp, TopologicalSpace.IsTopologicalBasis.mem_nhds_iff