Goal:
  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
  ============================
   (let H := CoreTactics.block in
    noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
intros _

Goals:
  
  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
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
CoreTactics.unblock_goal

Goals:
  
  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
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
unfold CoreTactics.block in *; cbv zeta

Goals:
  
  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
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
unfold CoreTactics.block in *

Goals:
  
  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
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
cbv zeta

Goals:
  
  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
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : NoConfusion_OnOne2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
simpl in * |-

Goals:
  
  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
  e : {|
        pr1 := hd; pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : {|
        pr1 := hd; pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := tl0; pr2 := {| pr1 := tl'0; pr2 := b |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
CoreTactics.on_last_hyp
            ltac:(fun id =>
                    hnf in id; CoreTactics.destruct_tele_eq id || destruct id)

Goals:
  
  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
  e : {|
        pr1 := hd; pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : {|
        pr1 := hd; pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := tl0; pr2 := {| pr1 := tl'0; pr2 := b |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
fun tac => lazymatch goal with
                      | H:_ |- _ => tac H
                      end

Goals:
  
  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
  e : {|
        pr1 := hd; pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : {|
        pr1 := hd; pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := tl0; pr2 := {| pr1 := tl'0; pr2 := b |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
fun id =>
             hnf in id; CoreTactics.destruct_tele_eq id || destruct id

Goals:
  
  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
  e : {|
        pr1 := hd; pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := hd'0; pr2 := {| pr1 := tl0; pr2 := p0 |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
        pr2 := OnOne2_tl P hd0 tl0 tl' b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
           pr2 := OnOne2_tl P hd0 tl0 tl' b
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  e : False
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
        pr2 := OnOne2_hd P hd0 hd' tl0 p
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
           pr2 := OnOne2_hd P hd0 hd' tl0 p
         |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  e : {|
        pr1 := hd; pr2 := {| pr1 := tl; pr2 := {| pr1 := tl'; pr2 := a |} |}
      |} =
      {|
        pr1 := hd0;
        pr2 := {| pr1 := tl0; pr2 := {| pr1 := tl'0; pr2 := b |} |}
      |}
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
        pr2 := OnOne2_tl P hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
           pr2 := OnOne2_tl P hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
           pr2 := OnOne2_tl P hd0 tl0 tl'0 b
         |} e) = e)


DEBUG:Going to execute:
lazymatch goal with
           | H:_ |- _ => tac H
           end