Goal:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2i P (S i0) tl0 tl'0
  H : sigma
        (λ i : nat,
           sigma
             (λ _ : A,
                sigma
                  (λ tl : list A,
                     sigma (λ tl' : list A, OnOne2i P (S i) tl tl'))))
  e : {|
        pr1 := i;
        pr2 :=
          {|
            pr1 := hd;
            pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
          |}
      |} = H
  ============================
   (noConfusion_OnOne2i_obligation_2 A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 :=
          {|
            pr1 := pr1 H;
            pr2 :=
              {|
                pr1 := pr1 (pr2 H) :: pr1 (pr2 (pr2 H));
                pr2 := pr1 (pr2 H) :: pr1 (pr2 (pr2 (pr2 H)))
              |}
          |};
        pr2 :=
          OnOne2i_tl P (pr1 H) (pr1 (pr2 H)) (pr1 (pr2 (pr2 H)))
            (pr1 (pr2 (pr2 (pr2 H)))) (pr2 (pr2 (pr2 (pr2 H))))
      |}
      (noConfusion_OnOne2i_obligation_1 A P
         {|
           pr1 :=
             {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
           pr2 := OnOne2i_tl P i hd tl tl' a
         |}
         {|
           pr1 :=
             {|
               pr1 := pr1 H;
               pr2 :=
                 {|
                   pr1 := pr1 (pr2 H) :: pr1 (pr2 (pr2 H));
                   pr2 := pr1 (pr2 H) :: pr1 (pr2 (pr2 (pr2 H)))
                 |}
             |};
           pr2 :=
             OnOne2i_tl P (pr1 H) (pr1 (pr2 H)) (pr1 (pr2 (pr2 H)))
               (pr1 (pr2 (pr2 (pr2 H)))) (pr2 (pr2 (pr2 (pr2 H))))
         |} e) = e)


DEBUG:Going to execute:
destruct H