Module: Mathlib.CategoryTheory.Limits.Constructions.Over.Products

Goal state before:
pp: J : Type w
C : Type u
inst✝ : Category.{v, u} C
X Y Z : C
f : X ⟶ Y
g : X ⟶ Z
c : PushoutCocone f g
⊢ { obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
            map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯, map_comp := ⋯ }.map
        ((NatIso.ofComponents (fun c ↦ c.eta) ⋯).hom.app c) ≫
      (NatIso.ofComponents
              (fun X_1 ↦
                BinaryCofan.ext
                  (Under.isoMk
                    (Iso.refl
                      (({ obj := fun c ↦ PushoutCocone.mk (Under.Hom.right c.inl) (Under.Hom.right c.inr) ⋯,
                                  map := fun {c₁ c₂} a ↦ { hom := Under.Hom.right a.hom, w := ⋯ }, map_id := ⋯,
                                  map_comp := ⋯ } ⋙
                                { obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
                                  map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯,
                                  map_comp := ⋯ }).obj
                            X_1).pt.right)
                    ⋯)
                  ⋯ ⋯)
              ⋯).hom.app
        ({ obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
              map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯, map_comp := ⋯ }.obj
          c) =
    𝟙
      ({ obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
            map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯, map_comp := ⋯ }.obj
        c)

Tactic:
ext

Goal state after:
J : Type w
C : Type u
inst✝ : Category.{v, u} C
X Y Z : C
f : X ⟶ Y
g : X ⟶ Z
c : PushoutCocone f g
⊢ Under.Hom.right
      ({ obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
                map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯, map_comp := ⋯ }.map
            ((NatIso.ofComponents (fun c ↦ c.eta) ⋯).hom.app c) ≫
          (NatIso.ofComponents
                  (fun X_1 ↦
                    BinaryCofan.ext
                      (Under.isoMk
                        (Iso.refl
                          (({ obj := fun c ↦ PushoutCocone.mk (Under.Hom.right c.inl) (Under.Hom.right c.inr) ⋯,
                                      map := fun {c₁ c₂} a ↦ { hom := Under.Hom.right a.hom, w := ⋯ }, map_id := ⋯,
                                      map_comp := ⋯ } ⋙
                                    { obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
                                      map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯,
                                      map_comp := ⋯ }).obj
                                X_1).pt.right)
                        ⋯)
                      ⋯ ⋯)
                  ⋯).hom.app
            ({ obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
                  map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯, map_comp := ⋯ }.obj
              c)).hom =
    Under.Hom.right
      (𝟙
          ({ obj := fun c ↦ BinaryCofan.mk (Under.homMk c.inl ⋯) (Under.homMk c.inr ⋯),
                map := fun {c₁ c₂} a ↦ { hom := Under.homMk a.hom ⋯, w := ⋯ }, map_id := ⋯, map_comp := ⋯ }.obj
            c)).hom