Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  b : B
  bs0 : list B
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b1 : OnOne2All P bs0 tl0 tl'0
  H : sigma
        (λ _ : B,
           sigma
             (λ bs : list B,
                sigma
                  (λ _ : A,
                     sigma
                       (λ tl : list A,
                          sigma (λ tl' : list A, OnOne2All P bs tl tl')))))
  e : {|
        pr1 := b0;
        pr2 :=
          {|
            pr1 := bs;
            pr2 :=
              {|
                pr1 := hd;
                pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
              |}
          |}
      |} = H
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 :=
          {|
            pr1 := pr1 H :: pr1 (pr2 H);
            pr2 :=
              {|
                pr1 := pr1 (pr2 (pr2 H)) :: pr1 (pr2 (pr2 (pr2 H)));
                pr2 := pr1 (pr2 (pr2 H)) :: pr1 (pr2 (pr2 (pr2 (pr2 H))))
              |}
          |};
        pr2 :=
          OnOne2All_tl P (pr1 H) (pr1 (pr2 H)) (pr1 (pr2 (pr2 H)))
            (pr1 (pr2 (pr2 (pr2 H)))) (pr1 (pr2 (pr2 (pr2 (pr2 H)))))
            (pr2 (pr2 (pr2 (pr2 (pr2 H)))))
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' a
         |}
         {|
           pr1 :=
             {|
               pr1 := pr1 H :: pr1 (pr2 H);
               pr2 :=
                 {|
                   pr1 := pr1 (pr2 (pr2 H)) :: pr1 (pr2 (pr2 (pr2 H)));
                   pr2 := pr1 (pr2 (pr2 H)) :: pr1 (pr2 (pr2 (pr2 (pr2 H))))
                 |}
             |};
           pr2 :=
             OnOne2All_tl P (pr1 H) (pr1 (pr2 H)) 
               (pr1 (pr2 (pr2 H))) (pr1 (pr2 (pr2 (pr2 H))))
               (pr1 (pr2 (pr2 (pr2 (pr2 H)))))
               (pr2 (pr2 (pr2 (pr2 (pr2 H)))))
         |} e) = e)


DEBUG:Going to execute:
destruct H