-- 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
⊢ Eq.{u + 1} (α := X _⦋1⦌)
    (Path.arrow
      ((sx.spineEquiv i : (a : X _⦋i⦌) → X.Path 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 := ⋯ }) :
          X _⦋i⦌))
      k)
    (Path.arrow
      ((sx.spineEquiv i : (a : X _⦋i⦌) → X.Path 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 :
          X _⦋i⦌))
      k)
have h : Eq (α := X _⦋1⦌)
  ((ConcreteCategory.hom (FC := TypeCat.Fun) (X.map (mkOfSucc k).op) : (a : X _⦋i⦌) → X _⦋1⦌)
      ((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 sorry).op)) :
                    (a : s.pt) → X _⦋1⦌)
                  x,
              arrow_src := sorry, arrow_tgt := sorry }) :
        X _⦋i⦌) :
    X _⦋1⦌)
  ((ConcreteCategory.hom (FC := TypeCat.Fun) (X.map (mkOfSucc k).op) : (a : X _⦋i⦌) → X _⦋1⦌)
      (((@ConcreteCategory.hom _ types TypeCat.Fun _ _ _ _ _ (s.π.app (StructuredArrow.mk (op f))) :
              TypeCat.Fun s.pt (X _⦋i⦌)) :
            (a : s.pt) → X _⦋i⦌)
          x :
        X _⦋i⦌) :
    X _⦋1⦌)
Tactic: dsimp only [spineEquiv, Equiv.coe_fn_mk, spine_arrow]