Goal:
    A : Type  P : list A → A → Type  l : list A  a : All_fold P l
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P l a a
      (noConfusionHom_All_fold_obligation_2 A P l a a eq_refl) = eq_refl)


DEBUG:Going to execute:
destruct p

Goals:
    A : Type  P : list A → A → Type
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P)
      (All_fold_nil P)
      (noConfusionHom_All_fold_obligation_2 A P [] 
         (All_fold_nil P) (All_fold_nil P) eq_refl) = eq_refl)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P (d :: Γ) 
      (All_fold_cons P a p) (All_fold_cons P a p)
      (noConfusionHom_All_fold_obligation_2 A P (d :: Γ)
         (All_fold_cons P a p) (All_fold_cons P a p) eq_refl) = eq_refl)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  P : list A → A → Type
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P)
      (All_fold_nil P)
      (noConfusionHom_All_fold_obligation_2 A P [] 
         (All_fold_nil P) (All_fold_nil P) eq_refl) = eq_refl)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P (d :: Γ) 
      (All_fold_cons P a p) (All_fold_cons P a p)
      (noConfusionHom_All_fold_obligation_2 A P (d :: Γ)
         (All_fold_cons P a p) (All_fold_cons P a p) eq_refl) = eq_refl)


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
    A : Type  P : list A → A → Type
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P)
      (All_fold_nil P)
      (noConfusionHom_All_fold_obligation_2 A P [] 
         (All_fold_nil P) (All_fold_nil P) eq_refl) = eq_refl)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P (d :: Γ) 
      (All_fold_cons P a p) (All_fold_cons P a p)
      (noConfusionHom_All_fold_obligation_2 A P (d :: Γ)
         (All_fold_cons P a p) (All_fold_cons P a p) eq_refl) = eq_refl)


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
    A : Type  P : list A → A → Type
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P)
      (All_fold_nil P)
      (noConfusionHom_All_fold_obligation_2 A P [] 
         (All_fold_nil P) (All_fold_nil P) eq_refl) = eq_refl)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P (d :: Γ) 
      (All_fold_cons P a p) (All_fold_cons P a p)
      (noConfusionHom_All_fold_obligation_2 A P (d :: Γ)
         (All_fold_cons P a p) (All_fold_cons P a p) eq_refl) = eq_refl)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  P : list A → A → Type
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P)
      (All_fold_nil P)
      (noConfusionHom_All_fold_obligation_2 A P [] 
         (All_fold_nil P) (All_fold_nil P) eq_refl) = eq_refl)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  ============================
   (let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    noConfusionHom_All_fold_obligation_1 A P (d :: Γ) 
      (All_fold_cons P a p) (All_fold_cons P a p)
      (noConfusionHom_All_fold_obligation_2 A P (d :: Γ)
         (All_fold_cons P a p) (All_fold_cons P a p) eq_refl) = eq_refl)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim