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'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
idtac
Level 2: Backtrace:

Tactic failure: No generalization needed.
Level 2: Backtrace:

Tactic failure: No generalization needed.
Level 2: Backtrace:

Tactic failure: No generalization needed.

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
tac H

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
DepElim.do_case hyp

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
fun p =>
             DepElim.introduce p;
              DepElim.elim_case p || destruct p || (case p; clear p)

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
DepElim.introduce p;
            DepElim.elim_case p || destruct p || (case p; clear p)

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
DepElim.introduce p
Level 4: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue

Level 4: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue


Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
fun p => first
             [ match p with
               | _ => generalize dependent p; intros p
               end
             | intros
             until
             p
             | intros
             until
             1
             | intros ]

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
        pr2 := OnOne2i_hd P i hd hd' tl p
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (let H := CoreTactics.block in
    NoConfusion_OnOne2i A P
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
    → let H0 := CoreTactics.block in
      {|
        pr1 := {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
        pr2 := OnOne2i_tl P i hd tl tl' a
      |} =
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |})


DEBUG:Going to execute:
first
[ match p with
  | _ => generalize dependent p; intros p
  end
| intros
until
p
| intros
until
1
| intros ]