-- Module: Mathlib.Algebra.Homology.CochainComplexOpposite
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : Preadditive.{v_1, u_1} C
K L : CochainComplex.{v_1, u_1, 0} C ℤ
f g : K ⟶ L
h :
  Homotopy.{v_1, u_1, 0} (ι := ℤ) (V := Cᵒᵖ) (c := ComplexShape.up ℤ) (C :=
    Functor.obj (Equivalence.functor (opEquivalence C)) (op L)) (D :=
    Functor.obj (Equivalence.functor (opEquivalence C)) (op K))
    (CategoryTheory.Functor.map (Equivalence.functor (opEquivalence C)) f.op)
    (CategoryTheory.Functor.map (Equivalence.functor (opEquivalence C)) g.op)
H :
  ∀ (p q p' q' : ℤ) (hp : p = p') (hq : q = q'),
    h.hom p q =
      Quiver.Hom.op (Iso.hom (HomologicalComplex.XIsoOfEq L ⋯)) ≫
        h.hom p' q' ≫ Quiver.Hom.op (Iso.hom (HomologicalComplex.XIsoOfEq K ⋯))
n : ℤ
⊢ HomologicalComplex.Hom.f (CategoryTheory.Functor.map (Equivalence.functor (opEquivalence C)) f.op) n =
    HAdd.hAdd (α :=
        (Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X n ⟶
          (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X n)
        (β :=
        (Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X n ⟶
          (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X n)
        (((dNext.{v_1, u_1, 0} (V := Cᵒᵖ) (c := ComplexShape.up ℤ) (C :=
                  Functor.obj (Equivalence.functor (opEquivalence C)) (op L)) (D :=
                  Functor.obj (Equivalence.functor (opEquivalence C)) (op K)) n :
                ((i j : ℤ) →
                    (Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X i ⟶
                      (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X j) →+
                  ((Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X n ⟶
                    (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X n)) :
              (a :
                  (i j : ℤ) → ((opEquivalence C).functor.obj (op L)).X i ⟶ ((opEquivalence C).functor.obj (op K)).X j) →
                ((opEquivalence C).functor.obj (op L)).X n ⟶ ((opEquivalence C).functor.obj (op K)).X n)
            h.hom :
          (Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X n ⟶
            (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X n)
        (((prevD.{v_1, u_1, 0} (V := Cᵒᵖ) (c := ComplexShape.up ℤ) (C :=
                  Functor.obj (Equivalence.functor (opEquivalence C)) (op L)) (D :=
                  Functor.obj (Equivalence.functor (opEquivalence C)) (op K)) n :
                ((i j : ℤ) →
                    (Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X i ⟶
                      (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X j) →+
                  ((Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X n ⟶
                    (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X n)) :
              (a :
                  (i j : ℤ) → ((opEquivalence C).functor.obj (op L)).X i ⟶ ((opEquivalence C).functor.obj (op K)).X j) →
                ((opEquivalence C).functor.obj (op L)).X n ⟶ ((opEquivalence C).functor.obj (op K)).X n)
            h.hom :
          (Functor.obj (Equivalence.functor (opEquivalence C)) (op L)).X n ⟶
            (Functor.obj (Equivalence.functor (opEquivalence C)) (op K)).X n) +
      HomologicalComplex.Hom.f (CategoryTheory.Functor.map (Equivalence.functor (opEquivalence C)) g.op) n

Tactic:
have := h.comm n