Goal:
  
  A : Type
  P : list A → A → Type
  l : list A
  a : All_fold P l
  b : All_fold P l
  e : NoConfusionHom_All_fold A P l a b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P l a b
      (noConfusionHom_All_fold_obligation_1 A P l a b e) = e)


DEBUG:Going to execute:
destruct a
Level 3: evaluation returns
idtac of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
DepElim.depelim b

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim
Level 4: 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 := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue

Level 4: 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 := b
       of type
       constr
of type
tacvalue
H := b
of type
constr 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 := b
       of type
       constr
of type
tacvalue
H := b
of type
constr 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 := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H
Level 3: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
DepElim.do_intros H

Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


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
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
try intros until H; intro_block_id H || intro_block H
Level 3: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := b
of type
constr of type tacvalue

Level 3: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := b
of type
constr of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  b : All_fold P []
  e : NoConfusionHom_All_fold A P [] (All_fold_nil P) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P [] (All_fold_nil P) b
      (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b e) = e)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b : All_fold P (d :: Γ)
  e : NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b
  ============================
   (noConfusionHom_All_fold_obligation_2 A P (d :: Γ) 
      (All_fold_cons P a p) b
      (noConfusionHom_All_fold_obligation_1 A P (d :: Γ)
         (All_fold_cons P a p) b e) = e)


DEBUG:Going to execute:
try intros until H