Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  b : B
  bs0 : list B
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P b hd0 hd'0
  e : #|bs0| = #|tl0|
  H : sigma
        (λ b : B,
           sigma
             (λ bs : list B,
                sigma
                  (λ hd : A,
                     sigma
                       (λ hd' : A,
                          sigma
                            (λ tl : list A,
                               sigma (λ _ : P b hd hd', #|bs| = #|tl|))))))
  e1 : {|
         pr1 := b0;
         pr2 :=
           {|
             pr1 := bs;
             pr2 :=
               {|
                 pr1 := hd;
                 pr2 :=
                   {|
                     pr1 := hd';
                     pr2 := {| pr1 := tl; pr2 := {| pr1 := p; pr2 := e0 |} |}
                   |}
               |}
           |}
       |} = H
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 :=
          {|
            pr1 := pr1 H :: pr1 (pr2 H);
            pr2 :=
              {|
                pr1 := pr1 (pr2 (pr2 H)) :: pr1 (pr2 (pr2 (pr2 (pr2 H))));
                pr2 :=
                  pr1 (pr2 (pr2 (pr2 H))) :: pr1 (pr2 (pr2 (pr2 (pr2 H))))
              |}
          |};
        pr2 :=
          OnOne2All_hd P (pr1 H) (pr1 (pr2 H)) (pr1 (pr2 (pr2 H)))
            (pr1 (pr2 (pr2 (pr2 H)))) (pr1 (pr2 (pr2 (pr2 (pr2 H)))))
            (pr1 (pr2 (pr2 (pr2 (pr2 (pr2 H))))))
            (pr2 (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_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 :=
             {|
               pr1 := pr1 H :: pr1 (pr2 H);
               pr2 :=
                 {|
                   pr1 := pr1 (pr2 (pr2 H)) :: pr1 (pr2 (pr2 (pr2 (pr2 H))));
                   pr2 :=
                     pr1 (pr2 (pr2 (pr2 H))) :: pr1 (pr2 (pr2 (pr2 (pr2 H))))
                 |}
             |};
           pr2 :=
             OnOne2All_hd P (pr1 H) (pr1 (pr2 H)) 
               (pr1 (pr2 (pr2 H))) (pr1 (pr2 (pr2 (pr2 H))))
               (pr1 (pr2 (pr2 (pr2 (pr2 H)))))
               (pr1 (pr2 (pr2 (pr2 (pr2 (pr2 H))))))
               (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 H))))))
         |} e1) = e1)


DEBUG:Going to execute:
destruct H