Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


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 4: type of id
 has value 
(list A)


Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
tac H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.do_case hyp

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


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

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


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

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


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 : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


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 : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


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