Goal:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  l0 : list A
  l : list B
  a : All2i R n l0 l
  b : All2i R n l0 l
  e : NoConfusionHom_All2i A B R n l0 l a b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n l0 l a b
      (noConfusionHom_All2i_obligation_1 A B R n l0 l a b e) = e)


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


Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


DEBUG:Going to execute:
DepElim.depelim b

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) 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
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) 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
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


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

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) 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
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


DEBUG:Going to execute:
DepElim.do_intros H

Goals:
  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) 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
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) 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
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) 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
  B : Type
  R : nat → A → B → Type
  n : nat
  b : All2i R n [] []
  e : NoConfusionHom_All2i A B R n [] [] All2i_nil b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n [] [] All2i_nil b
      (noConfusionHom_All2i_obligation_1 A B R n [] [] All2i_nil b e) = e)

  
  A : Type
  B : Type
  R : nat → A → B → Type
  n : nat
  x : A
  y : B
  l : list A
  r : list B
  r0 : R n x y
  a : All2i R (S n) l r
  b : All2i R n (x :: l) (y :: r)
  e : NoConfusionHom_All2i A B R n (x :: l) (y :: r) (All2i_cons r0 a) b
  ============================
   (noConfusionHom_All2i_obligation_2 A B R n (x :: l) 
      (y :: r) (All2i_cons r0 a) b
      (noConfusionHom_All2i_obligation_1 A B R n (x :: l) 
         (y :: r) (All2i_cons r0 a) b e) = e)


DEBUG:Going to execute:
try intros until H