Goal:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


DEBUG:Going to execute:
cbv beta iota delta [TODO projection TODO projection] in id, id'
DEBUG LTAC Evaluated term: H1
DEBUG LTAC Evaluated term: (list A)
Level 3: type of id
 has value 
(list A)


Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


DEBUG:Going to execute:
tac H

Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


DEBUG:Going to execute:
DepElim.do_case hyp

Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


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

Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


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

Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


DEBUG:Going to execute:
DepElim.introduce p
Level 2: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := H
of type
ident of type tacvalue

Level 2: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := H
of type
ident of type tacvalue


Goals:
  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


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 : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd' :: tl))

  
  A : Type
  P : A → A → Type
  Q : A → Type
  HPQ : ∀ x y : A, Q x → P x y → Q y
  hd : A
  tl : list A
  tl' : list A
  X : OnOne2 P tl tl'
  IHX : All Q tl → All Q tl'
  H1 : list A
  H : All Q H1
  ============================
   (hd :: tl = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All Q (hd :: tl'))


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