Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  l : list A
  l' : list B
  ============================
   (All2 P l l' → All2 Q l l' → All2 (Trel_conj P Q) l l')


DEBUG:Going to execute:
induction 1

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type
  ============================
   (All2 Q [] [] → 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'
  ============================
   (All2 Q (x :: l) (y :: l') → All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
intros H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
depelim H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
fun H => DepElim.depelim H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.depelim H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
fun id =>
             DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
fun tac H =>
             DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
              CoreTactics.unblock_goal

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
fun hyp => DepElim.do_case hyp

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
            CoreTactics.unblock_goal

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim
Level 3: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 3: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue


Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
fun tac H =>
             DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H
Level 1: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue


Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
DepElim.do_intros H

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
fun H =>
             try intros until H; intro_block_id H || intro_block H;
              (try simpl in H; DepElim.simplify_equations_in H)

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
try intros until H; intro_block_id H || intro_block H;
            (try simpl in H; DepElim.simplify_equations_in H)

Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
try intros until H; intro_block_id H || intro_block H
Level 1: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := H
of type
ident of type tacvalue


Goals:
    A : Type  B : Type  P : A → B → Type  Q : A → B → Type  H : All2 Q [] []
  ============================
   (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'
  H : All2 Q (x :: l) (y :: l')
  ============================
   (All2 (Trel_conj P Q) (x :: l) (y :: l'))


DEBUG:Going to execute:
try intros until H