Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  H : sigma
        (λ d : A,
           sigma
             (λ d' : A,
                sigma
                  (λ Γ : list A,
                     sigma
                       (λ Γ' : list A,
                          sigma (λ _ : All2_fold P Γ Γ', P Γ Γ' d d')))))
  e : {|
        pr1 := d;
        pr2 :=
          {|
            pr1 := d';
            pr2 :=
              {|
                pr1 := Γ;
                pr2 := {| pr1 := Γ'; pr2 := {| pr1 := a; pr2 := p |} |}
              |}
          |}
      |} = H
  ============================
   (noConfusion_All2_fold_obligation_2 A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 :=
          {|
            pr1 := pr1 H :: pr1 (pr2 (pr2 H));
            pr2 := pr1 (pr2 H) :: pr1 (pr2 (pr2 (pr2 H)))
          |};
        pr2 :=
          All2_fold_cons P (pr1 (pr2 (pr2 (pr2 (pr2 H)))))
            (pr2 (pr2 (pr2 (pr2 (pr2 H)))))
      |}
      (noConfusion_All2_fold_obligation_1 A P
         {|
           pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
           pr2 := All2_fold_cons P a p
         |}
         {|
           pr1 :=
             {|
               pr1 := pr1 H :: pr1 (pr2 (pr2 H));
               pr2 := pr1 (pr2 H) :: pr1 (pr2 (pr2 (pr2 H)))
             |};
           pr2 :=
             All2_fold_cons P (pr1 (pr2 (pr2 (pr2 (pr2 H)))))
               (pr2 (pr2 (pr2 (pr2 (pr2 H)))))
         |} e) = e)


DEBUG:Going to execute:
destruct H