-- Module: Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : Preadditive.{v_1, u_1} C
inst_2 : HasZeroObject.{v_1, u_1} C
inst_3 : HasShift.{v_1, u_1, 0} C ℤ
inst_4 : ∀ (n : ℤ), Functor.Additive.{v_1, u_1, v_1, u_1} (shiftFunctor C n)
inst_5 : Pretriangulated.{v_1, u_1} C
t : TStructure.{v_1, u_1} C
⊢ Eq (α :=
    Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
      (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
        Functor.{v_1, v_1, u_1, u_1} C C)
      (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
        Functor.{v_1, v_1, u_1, u_1} C C))
    (WithBotTop.rec (motive := fun {x : EInt} ↦
        (f : x ⟶ ⊤) →
          Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
            (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) x :
              Functor.{v_1, v_1, u_1, u_1} C C)
            (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
              Functor.{v_1, v_1, u_1, u_1} C C))
        (fun (f : Quiver.Hom (V := EInt) ⊥ ⊤) ↦
          WithBotTop.rec (motive := fun {y : EInt} ↦
            (f : ⊥ ⟶ y) →
              Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                    ⊥ :
                  Functor.{v_1, v_1, u_1, u_1} C C)
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                    y :
                  Functor.{v_1, v_1, u_1, u_1} C C))
            (fun (f : Quiver.Hom (V := EInt) ⊥ ⊥) ↦
              𝟙
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                  ⊥))
            (fun (b : ℤ) (f : ⊥ ⟶ WithBotTop.coe b) ↦ 0) (fun (f : Quiver.Hom (V := EInt) ⊥ ⊤) ↦ 0) ⊤ f)
        (fun (a : ℤ) (f : WithBotTop.coe a ⟶ ⊤) ↦
          WithBotTop.rec (motive := fun {y : EInt} ↦
            (f : WithBotTop.coe a ⟶ y) →
              Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                    (WithBotTop.coe a) :
                  Functor.{v_1, v_1, u_1, u_1} C C)
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                    y :
                  Functor.{v_1, v_1, u_1, u_1} C C))
            (fun (f : WithBotTop.coe a ⟶ ⊥) ↦ 0)
            (fun (b : ℤ) (f : WithBotTop.coe a ⟶ WithBotTop.coe b) ↦ t.natTransTruncLTOfLE a b ⋯)
            (fun (f : WithBotTop.coe a ⟶ ⊤) ↦ t.truncLTι a) ⊤ f)
        (fun (f : Quiver.Hom (V := EInt) ⊤ ⊤) ↦
          WithBotTop.rec (motive := fun {y : EInt} ↦
            (f : ⊤ ⟶ y) →
              Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                    ⊤ :
                  Functor.{v_1, v_1, u_1, u_1} C C)
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                    y :
                  Functor.{v_1, v_1, u_1, u_1} C C))
            (fun (f : Quiver.Hom (V := EInt) ⊤ ⊥) ↦ 0) (fun (b : ℤ) (f : ⊤ ⟶ WithBotTop.coe b) ↦ 0)
            (fun (f : Quiver.Hom (V := EInt) ⊤ ⊤) ↦
              𝟙
                (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C)
                  ⊤))
            ⊤ f)
        ⊤ (𝟙 ⊤) :
      Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
        (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
          Functor.{v_1, v_1, u_1, u_1} C C)
        (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
          Functor.{v_1, v_1, u_1, u_1} C C))
    (𝟙 (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤) :
      Quiver.Hom (V := Functor.{v_1, v_1, u_1, u_1} C C)
        (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
          Functor.{v_1, v_1, u_1, u_1} C C)
        (WithBotTop.rec (motive := fun (x : WithBotTop ℤ) ↦ Functor.{v_1, v_1, u_1, u_1} C C) 0 t.truncLT (𝟭 C) ⊤ :
          Functor.{v_1, v_1, u_1, u_1} C C))

Tactic:
simp