-- Lean 4 proof step from Mathlib.CategoryTheory.Limits.Shapes.Equalizers (goal)
Goal:
C : Type u
inst : Category.{v, u} C
X_1 Y_1 : C
f_1 g : X_1 ⟶ Y_1
P : C
ι : P ⟶ X_1
w : ι ≫ f_1 = ι ≫ g
X Y : WalkingParallelPair
f : X ⟶ Y
⊢ Eq.{v + 1} (α :=
    Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj Y)
    (Functor.map (Functor.obj (Functor.const WalkingParallelPair) P) f ≫
      WalkingParallelPair.casesOn (motive := fun (t : WalkingParallelPair) ↦
        (h : Y = t) →
          Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) Y ⟶ (parallelPair f_1 g).obj Y)
        Y
        (fun (h : Y = zero) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            ι ⋯)
        (fun (h : Y = one) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            (ι ≫ f_1) ⋯)
        ⋯)
    (WalkingParallelPair.casesOn (motive := fun (t : WalkingParallelPair) ↦
        (h : X = t) →
          Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
        X
        (fun (h : X = zero) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            ι ⋯)
        (fun (h : X = one) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            (ι ≫ f_1) ⋯)
        ⋯ ≫
      (parallelPair f_1 g).map f)
have zero : ∀ (f : zero ⟶ Y),
  Eq.{v + 1} (α :=
    Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) zero ⟶ (parallelPair f_1 g).obj Y)
    (Functor.map (Functor.obj (Functor.const WalkingParallelPair) P) f ≫
      WalkingParallelPair.casesOn (motive := fun (t : WalkingParallelPair) ↦
        (h : Y = t) →
          Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) Y ⟶ (parallelPair f_1 g).obj Y)
        Y
        (fun (h : Y = zero) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            ι sorry)
        (fun (h : Y = one) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            (ι ≫ f_1) sorry)
        sorry)
    (WalkingParallelPair.casesOn (motive := fun (t : WalkingParallelPair) ↦
        (h : zero = t) →
          Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) zero ⟶
            (parallelPair f_1 g).obj zero)
        zero
        (fun (h : zero = zero) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            ι sorry)
        (fun (h : zero = one) ↦
          Eq.ndrec (motive := fun (X : WalkingParallelPair) ↦
            Functor.obj.{0, v, 0, u} (Functor.obj (Functor.const WalkingParallelPair) P) X ⟶ (parallelPair f_1 g).obj X)
            (ι ≫ f_1) sorry)
        sorry ≫
      (parallelPair f_1 g).map f)
Tactic: cases X
Cleared hypotheses: X, f