Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


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 B)
Level 4: type of id
 has value 
(list B)


Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
tac H

Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_case hyp

Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


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

Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


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

Goals:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


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
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


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
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := []; pr2 := [] |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])

  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q H1' H1
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (y :: l'))


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