-- Module: Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : Abelian.{v, u} C
inst_2 : HasExt.{w, v, u} C
S : ShortComplex.{v, u} C
hS : S.ShortExact
Y : C
n₀ n₁ : ℕ
h : 1 + n₀ = n₁
this_1 : HasDerivedCategory C := HasDerivedCategory.standard C
this : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)
x : Ext.{w, v, u} S.X₃ Y n₁
⊢ Eq (α :=
    ShiftedHom (C := DerivedCategory C) (M := ℤ) (Functor.obj (singleFunctor C 0) S.X₂)
      (Functor.obj (singleFunctor C 0) Y) (↑n₁ : ℤ))
    (((ConcreteCategory.hom (FC := fun (x1 x2 : AddCommGrpCat) ↦ (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v)))
                (CC := AddCommGrpCat.carrier)
                (ShortComplex.mk (X₁ :=
                    Functor.obj (C := (DerivedCategory C)ᵒᵖ)
                      (Functor.shift (Functor.obj preadditiveYoneda (Functor.obj (singleFunctor C 0) Y)) (M := ℤ)
                        (↑n₀ : ℤ))
                      (Triangle.obj₃
                        (Functor.obj (Equivalence.functor (triangleOpEquivalence (DerivedCategory C)))
                          (op hS.singleTriangle))))
                    (Functor.homologySequenceδ (Functor.obj preadditiveYoneda (Functor.obj (singleFunctor C 0) Y))
                      (Functor.obj (Equivalence.functor (triangleOpEquivalence (DerivedCategory C)))
                        (op hS.singleTriangle))
                      (↑n₀ : ℤ) (↑n₁ : ℤ) ⋯)
                    (Functor.map
                      (Functor.shift (Functor.obj preadditiveYoneda (Functor.obj (singleFunctor C 0) Y)) (M := ℤ)
                        (↑n₁ : ℤ))
                      (Triangle.mor₁
                        (Functor.obj (Equivalence.functor (triangleOpEquivalence (DerivedCategory C)))
                          (op hS.singleTriangle))))
                    ⋯).g).comp
            (↑homAddEquiv :
              Ext S.X₃ Y n₁ →+ ShiftedHom ((singleFunctor C 0).obj S.X₃) ((singleFunctor C 0).obj Y) (↑n₁ : ℤ)) :
          (a : Ext S.X₃ Y n₁) → ShiftedHom ((singleFunctor C 0).obj S.X₂) ((singleFunctor C 0).obj Y) (↑n₁ : ℤ))
        x :
      ShiftedHom (C := DerivedCategory C) (M := ℤ) (Functor.obj (singleFunctor C 0) S.X₂)
        (Functor.obj (singleFunctor C 0) Y) (↑n₁ : ℤ))
    ((AddMonoidHom.comp
            (↑homAddEquiv :
              Ext S.X₂ Y n₁ →+ ShiftedHom ((singleFunctor C 0).obj S.X₂) ((singleFunctor C 0).obj Y) (↑n₁ : ℤ))
            (ConcreteCategory.hom (FC := fun (x1 x2 : AddCommGrpCat.{w}) ↦ (↑x1 : Type w) →+ (↑x2 : Type w)) (CC :=
              AddCommGrpCat.carrier)
              (ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} S.X₁ Y n₀))
                  (AddCommGrpCat.ofHom (precomp hS.extClass Y h)) (AddCommGrpCat.ofHom (precomp (mk₀ S.g) Y ⋯)) ⋯).g) :
          (a : Ext S.X₃ Y n₁) → ShiftedHom ((singleFunctor C 0).obj S.X₂) ((singleFunctor C 0).obj Y) (↑n₁ : ℤ))
        x :
      ShiftedHom (C := DerivedCategory C) (M := ℤ) (Functor.obj (singleFunctor C 0) S.X₂)
        (Functor.obj (singleFunctor C 0) Y) (↑n₁ : ℤ))

Tactic:
apply singleFunctor_map_comp_hom (C := C)

Premises used: CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom