-- Lean 4 proof step from Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal (goal)
Goal:
X : SSet
sx : X.StrictSegal
n : ℕ
s :
  Cone (J := StructuredArrow (C := (SimplexCategory.Truncated 2)ᵒᵖ) (op ⦋n⦌) (Functor.op (inclusion 2)))
    (proj (op ⦋n⦌) (Functor.op (inclusion 2)) ⋙ Functor.op (inclusion 2) ⋙ X)
x : s.pt
i : ℕ
hi : i ≤ 2
f :
  unop
      (obj (C := (SimplexCategory.Truncated 2)ᵒᵖ) (Functor.op (inclusion 2))
        (op (ObjectProperty.FullSubcategory.mk (P := fun (a : SimplexCategory) ↦ a.len ≤ 2) ⦋i⦌ hi))) ⟶
    unop (op ⦋n⦌)
k : Fin (i + 1)
⊢ (X.spine i
          ((ConcreteCategory.hom (FC := TypeCat.Fun) (X.map (op f)) : (a : X _⦋n⦌) → X _⦋i⦌)
            (sx.spineToSimplex
              {
                vertex := fun (i : Fin (n + 1)) ↦
                  (@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _
                        (s.π.app
                          (StructuredArrow.mk (Y :=
                            op
                              (ObjectProperty.FullSubcategory.mk (P := fun (a : SimplexCategory) ↦ a.len ≤ 2) ⦋0⦌
                                lift._proof_2))
                            (Quiver.Hom.op (⦋0⦌.const ⦋n⦌ i)))) :
                      (a : s.pt) → X _⦋0⦌)
                    x,
                arrow := fun (i : Fin n) ↦
                  (@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _
                        (s.π.app
                          (StructuredArrow.mk (Y :=
                            op
                              (ObjectProperty.FullSubcategory.mk (P := fun (a : SimplexCategory) ↦ a.len ≤ 2) ⦋1⦌
                                lift._proof_4))
                            (mkOfLe i.castSucc i.succ ⋯).op)) :
                      (a : s.pt) → X _⦋1⦌)
                    x,
                arrow_src := ⋯, arrow_tgt := ⋯ :
                ((trunc 1 1 lift._proof_8).obj (obj (truncation 1) X)).Path₁ n }))).vertex
      k =
    (X.spine i
          (((@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _ (s.π.app (StructuredArrow.mk (op f))) :
                TypeCat.Fun s.pt (X _⦋i⦌)) :
              (a : s.pt) → X _⦋i⦌)
            x)).vertex
      k
have h : (X.spine i
        ((ConcreteCategory.hom (FC := TypeCat.Fun) (X.map f.op) : (a : X _⦋n⦌) → X _⦋i⦌)
          (sx.spineToSimplex
            {
              vertex := fun (i : Fin (n + 1)) ↦
                (@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _
                      (s.π.app
                        (StructuredArrow.mk (Y :=
                          op
                            (ObjectProperty.FullSubcategory.mk (P := fun (a : SimplexCategory) ↦ a.len ≤ 2) ⦋0⦌
                              lift._proof_2))
                          (Quiver.Hom.op (⦋0⦌.const ⦋n⦌ i)))) :
                    (a : s.pt) → X _⦋0⦌)
                  x,
              arrow := fun (i : Fin n) ↦
                (@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _
                      (s.π.app
                        (StructuredArrow.mk (Y :=
                          op
                            (ObjectProperty.FullSubcategory.mk (P := fun (a : SimplexCategory) ↦ a.len ≤ 2) ⦋1⦌
                              lift._proof_4))
                          (mkOfLe i.castSucc i.succ sorry).op)) :
                    (a : s.pt) → X _⦋1⦌)
                  x,
              arrow_src := sorry, arrow_tgt := sorry :
              ((trunc 1 1 lift._proof_8).obj (obj (truncation 1) X)).Path₁ n }))).vertex
    k =
  (X.spine i
        (((@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _
                (s.π.app
                  (StructuredArrow.mk (Y :=
                    op (ObjectProperty.FullSubcategory.mk (P := fun (a : SimplexCategory) ↦ a.len ≤ 2) ⦋i⦌ hi)) f.op)) :
              TypeCat.Fun s.pt (X _⦋i⦌)) :
            (a : s.pt) → X _⦋i⦌)
          x)).vertex
    k
Tactic: rw [dsimp% show op f = f.op from rfl]