-- Module: Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks
Goal:
C : Type u₁
inst : Category.{v₁, u₁} C
J : Type u₂
inst_1 : Category.{v₂, u₂} J
X Y Z : Cᵒᵖ
f_1 : X ⟶ Z
g : Y ⟶ Z
f : Option.none ⟶ some WalkingPair.left
none :
  Eq (α :=
    (span f_1.unop g.unop).obj Option.none ⟶
      obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) (some WalkingPair.left))
    ((span f_1.unop g.unop).map (WidePushoutShape.Hom.init WalkingPair.left) ≫
      Iso.hom
        ((fun (x : WalkingSpan) ↦
            (match (motive :=
                (x : WalkingSpan) →
                  (span f_1.unop g.unop).obj x ≅
                    obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x)
                x with
              | Option.none => Iso.refl ((span f_1.unop g.unop).obj Option.none)
              | some WalkingPair.left => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.left)
              | some WalkingPair.right => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.right) :
              (span f_1.unop g.unop).obj x ≅
                obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x))
          (some WalkingPair.left)))
    (Iso.hom
        ((fun (x : WalkingSpan) ↦
            (match (motive :=
                (x : WalkingSpan) →
                  (span f_1.unop g.unop).obj x ≅
                    obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x)
                x with
              | Option.none => Iso.refl ((span f_1.unop g.unop).obj Option.none)
              | some WalkingPair.left => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.left)
              | some WalkingPair.right => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.right) :
              (span f_1.unop g.unop).obj x ≅
                obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x))
          Option.none) ≫
      map (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) (WidePushoutShape.Hom.init WalkingPair.left))
⊢ Eq (α :=
    (span f_1.unop g.unop).obj Option.none ⟶
      obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) (some WalkingPair.left))
    ((span f_1.unop g.unop).map f ≫
      Iso.hom
        ((fun (x : WalkingSpan) ↦
            (match (motive :=
                (x : WalkingSpan) →
                  (span f_1.unop g.unop).obj x ≅
                    obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x)
                x with
              | Option.none => Iso.refl ((span f_1.unop g.unop).obj Option.none)
              | some WalkingPair.left => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.left)
              | some WalkingPair.right => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.right) :
              (span f_1.unop g.unop).obj x ≅
                obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x))
          (some WalkingPair.left)))
    (Iso.hom
        ((fun (x : WalkingSpan) ↦
            (match (motive :=
                (x : WalkingSpan) →
                  (span f_1.unop g.unop).obj x ≅
                    obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x)
                x with
              | Option.none => Iso.refl ((span f_1.unop g.unop).obj Option.none)
              | some WalkingPair.left => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.left)
              | some WalkingPair.right => Iso.refl ((span f_1.unop g.unop).obj WalkingSpan.right) :
              (span f_1.unop g.unop).obj x ≅
                obj.{0, v₁, 0, u₁} (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) x))
          Option.none) ≫
      map (walkingCospanOpEquiv.inverse ⋙ Functor.leftOp (cospan f_1 g)) f)

Tactic:
cases f