Goal:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  H := {|
         pr1 := hd0;
         pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
       |}
    : sigma (λ hd : A, sigma (λ hd' : A, sigma (λ _ : list A, P hd hd')))
  e : {|
        pr1 := hd; pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
      |} = H
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 :=
          {|
            pr1 := pr1 H :: pr1 (pr2 (pr2 H));
            pr2 := pr1 (pr2 H) :: pr1 (pr2 (pr2 H))
          |};
        pr2 :=
          OnOne2_hd P (pr1 H) (pr1 (pr2 H)) (pr1 (pr2 (pr2 H)))
            (pr2 (pr2 (pr2 H)))
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 :=
             {|
               pr1 := pr1 H :: pr1 (pr2 (pr2 H));
               pr2 := pr1 (pr2 H) :: pr1 (pr2 (pr2 H))
             |};
           pr2 :=
             OnOne2_hd P (pr1 H) (pr1 (pr2 H)) (pr1 (pr2 (pr2 H)))
               (pr2 (pr2 (pr2 H)))
         |} e) = e)


DEBUG:Going to execute:
clearbody rhs