∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [inst_1 : CategoryTheory.IsSplitMono f]
  (X_1 : CategoryTheory.Limits.WalkingParallelPair),
  (CategoryTheory.Limits.coneOfIsSplitMono f).π.app X_1 =
    CategoryTheory.Limits.WalkingParallelPair.casesOn (motive := fun t =>
      X_1 = t →
        (((CategoryTheory.Functor.const CategoryTheory.Limits.WalkingParallelPair).obj X).obj X_1 ⟶
          (CategoryTheory.Limits.parallelPair (CategoryTheory.CategoryStruct.id Y)
                (CategoryTheory.CategoryStruct.comp (CategoryTheory.retraction f) f)).obj
            X_1))
      X_1 (fun h => ⋯ ▸ f) (fun h => ⋯ ▸ CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.id Y)) ⋯