-- Module: Mathlib.AlgebraicTopology.SimplicialSet.Skeleton
Goal:
X Y : SSet
i : X ⟶ Y
d : ℕ
n : SimplexCategory
y : Y _⦋d⦌
hy₁ : y ∈ Y.nonDegenerate d
hy₂ : ∀ (x : X _⦋d⦌), ¬(ConcreteCategory.hom (FC := TypeCat.Fun) (i.app (op ⦋d⦌)) : (a : X _⦋d⦌) → Y _⦋d⦌) x = y
f : op ⦋d⦌ ⟶ op n
hx :
  Membership.mem (α := Y.obj (op n)) (γ := Set (Y.obj (op n)))
    (Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n))
    ((ConcreteCategory.hom (FC := TypeCat.Fun) (Y.map f) :
          (a : (fun (X : Type u) ↦ X) (Y _⦋d⦌)) → (fun (X : Type u) ↦ X) (Y.obj (op n)))
        y :
      (fun (X : Type u) ↦ X) (Y.obj (op n)))
h :
  Membership.mem (α := (Subcomplex.toSSet (X := Y) ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1))).obj (op n))
    (γ := Set ((Subcomplex.toSSet (X := Y) ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1))).obj (op n)))
    (Subfunctor.obj ⊤ (op n))
    (Subtype.mk (p := fun (x : Y.obj (op n)) ↦
        Membership.mem (γ := Set (Y.obj (op n)))
          (Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) x)
        ((ConcreteCategory.hom (FC := TypeCat.Fun) (Y.map f) :
            (a : (fun (X : Type u) ↦ X) (Y _⦋d⦌)) → (fun (X : Type u) ↦ X) (Y.obj (op n)))
          y)
        hx :
      { x : Y.obj (op n) //
        Membership.mem (γ := Set (Y.obj (op n)))
          (Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) x })
c : Cell i d := { simplex := y, nonDegenerate := hy₁, notMem := ⋯ }
⊢ Membership.mem (α := (↑(Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) : Type u)) (γ :=
    Set (↑(Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) : Type u))
    (Set.range (ι := (↑(Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) d) (op n)) : Type u))
        (⇑{
              toFun := fun (x : (↑(Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) d) (op n)) : Type u)) ↦
                Subtype.mk (p := fun (x : Y.obj (op n)) ↦
                  Membership.mem (γ := Set (Y.obj (op n)))
                    (Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) x)
                  (↑x : Y.obj (op n)) ⋯ } :
          (a : (↑(((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) d).obj (op n)) : Type u)) →
            (↑(((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)).obj (op n)) : Type u)) ∪
      Set.range (ι := (sigmaStdSimplex i d).obj (op n))
        (⇑(ConcreteCategory.hom (FC := TypeCat.Fun) ((b i d).app (op n))) :
          (a : (sigmaStdSimplex i d).obj (op n)) →
            (↑(((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)).obj (op n)) : Type u)))
    (Subtype.mk (p := fun (x : Y.obj (op n)) ↦
        Membership.mem (γ := Set (Y.obj (op n)))
          (Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) x)
        ((ConcreteCategory.hom (FC := TypeCat.Fun) (Y.map f) :
            (a : (fun (X : Type u) ↦ X) (Y _⦋d⦌)) → (fun (X : Type u) ↦ X) (Y.obj (op n)))
          y)
        hx :
      { x : Y.obj (op n) //
        Membership.mem (γ := Set (Y.obj (op n)))
          (Subfunctor.obj ((skeletonOfMono i : (a : ℕ) → Y.Subcomplex) (d + 1)) (op n)) x })

Tactic:
Or.inr ⟨c.ιSigmaStdSimplex.app _ (stdSimplex.objEquiv.symm f.unop), ?_⟩

Premises used: Set.union, CategoryTheory.ConcreteCategory.hom, Set.Mem, SSet.relativeCellComplexOfMono.Cell.ιSigmaStdSimplex, setOf, Quiver.Hom.unop, Exists.intro, Equiv.symm, DFunLike.coe, CategoryTheory.NatTrans.app, SSet.stdSimplex.objEquiv, Or.inr