-- Lean 4 proof step from Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences (hypothesis)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : Abelian.{v, u} C
inst_2 : HasExt.{w, v, u} C
X : C
S : ShortComplex.{v, u} C
hS : S.ShortExact
n₁ : ℕ
x₁ : Ext.{w, v, u} X S.X₁ n₁
hx₁ : x₁.comp (mk₀ S.f) ⋯ = 0
n₀ : ℕ
hn₀ : n₀ + 1 = n₁
this :
  (ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} X S.X₃ n₀)) (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀))
      (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X ⋯)) ⋯).Exact
⊢ ∃ (x₃ : Ext.{w, v, u} X S.X₃ n₀), x₃.comp hS.extClass hn₀ = x₁
have this₁ : ∀
  (x₂ :
    (↑(ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} X S.X₃ n₀))
            (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry)) sorry).X₂ :
      Type w)),
  Eq (α :=
      (↑(ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} X S.X₃ n₀))
              (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry)) sorry).X₃ :
        Type w))
      ((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} X S.X₃ n₀))
                  (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry))
                  sorry).g :
            (a :
                (↑{ X₁ := AddCommGrpCat.of (Ext X S.X₃ n₀), X₂ := AddCommGrpCat.of (Ext X S.X₁ n₁),
                        X₃ := AddCommGrpCat.of (Ext X S.X₂ n₁), f := AddCommGrpCat.ofHom (hS.extClass.postcomp X hn₀),
                        g := AddCommGrpCat.ofHom ((mk₀ S.f).postcomp X sorry), zero := sorry }.X₂ :
                  Type w)) →
              (↑{ X₁ := AddCommGrpCat.of (Ext X S.X₃ n₀), X₂ := AddCommGrpCat.of (Ext X S.X₁ n₁),
                      X₃ := AddCommGrpCat.of (Ext X S.X₂ n₁), f := AddCommGrpCat.ofHom (hS.extClass.postcomp X hn₀),
                      g := AddCommGrpCat.ofHom ((mk₀ S.f).postcomp X sorry), zero := sorry }.X₃ :
                Type w))
          x₂ :
        (↑(ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} X S.X₃ n₀))
                (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry))
                sorry).X₃ :
          Type w))
      (0 :
        (↑(ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} X S.X₃ n₀))
                (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry))
                sorry).X₃ :
          Type w)) →
    ∃ (x₁ :
      (↑(ShortComplex.mk (X₁ := AddCommGrpCat.of (Ext.{w, v, u} X S.X₃ n₀))
              (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry)) sorry).X₁ :
        Type w)),
      (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} X S.X₃ n₀))
                  (AddCommGrpCat.ofHom (postcomp hS.extClass X hn₀)) (AddCommGrpCat.ofHom (postcomp (mk₀ S.f) X sorry))
                  sorry).f :
            (a :
                (↑{ X₁ := AddCommGrpCat.of (Ext X S.X₃ n₀), X₂ := AddCommGrpCat.of (Ext X S.X₁ n₁),
                        X₃ := AddCommGrpCat.of (Ext X S.X₂ n₁), f := AddCommGrpCat.ofHom (hS.extClass.postcomp X hn₀),
                        g := AddCommGrpCat.ofHom ((mk₀ S.f).postcomp X sorry), zero := sorry }.X₁ :
                  Type w)) →
              (↑{ X₁ := AddCommGrpCat.of (Ext X S.X₃ n₀), X₂ := AddCommGrpCat.of (Ext X S.X₁ n₁),
                      X₃ := AddCommGrpCat.of (Ext X S.X₂ n₁), f := AddCommGrpCat.ofHom (hS.extClass.postcomp X hn₀),
                      g := AddCommGrpCat.ofHom ((mk₀ S.f).postcomp X sorry), zero := sorry }.X₂ :
                Type w))
          x₁ =
        x₂
Tactic: rw [ShortComplex.ab_exact_iff] at this
Cleared hypotheses: this