Goal:
  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  b' : list A
  b : All_fold P b'
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} = {| pr1 := b'; pr2 := b |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)


DEBUG:Going to execute:
destruct p

Goals:
    A : Type  P : list A → A → Type  b0 : All_fold P []
  ============================
   ({| pr1 := []; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  b0 : All_fold P []
  d : A
  Γ : list A
  b : All_fold P Γ
  p : P Γ d
  ============================
   ({| pr1 := []; pr2 := b0 |} =
    {| pr1 := d :: Γ; pr2 := All_fold_cons P b p |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  d0 : A
  Γ0 : list A
  b : All_fold P Γ0
  p0 : P Γ0 d0
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} =
    {| pr1 := d0 :: Γ0; pr2 := All_fold_cons P b p0 |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  P : list A → A → Type  b0 : All_fold P []
  ============================
   ({| pr1 := []; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  b0 : All_fold P []
  d : A
  Γ : list A
  b : All_fold P Γ
  p : P Γ d
  ============================
   ({| pr1 := []; pr2 := b0 |} =
    {| pr1 := d :: Γ; pr2 := All_fold_cons P b p |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  d0 : A
  Γ0 : list A
  b : All_fold P Γ0
  p0 : P Γ0 d0
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} =
    {| pr1 := d0 :: Γ0; pr2 := All_fold_cons P b p0 |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)


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

Goals:
    A : Type  P : list A → A → Type  b0 : All_fold P []
  ============================
   ({| pr1 := []; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  b0 : All_fold P []
  d : A
  Γ : list A
  b : All_fold P Γ
  p : P Γ d
  ============================
   ({| pr1 := []; pr2 := b0 |} =
    {| pr1 := d :: Γ; pr2 := All_fold_cons P b p |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  d0 : A
  Γ0 : list A
  b : All_fold P Γ0
  p0 : P Γ0 d0
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} =
    {| pr1 := d0 :: Γ0; pr2 := All_fold_cons P b p0 |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)


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

Goals:
    A : Type  P : list A → A → Type  b0 : All_fold P []
  ============================
   ({| pr1 := []; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  b0 : All_fold P []
  d : A
  Γ : list A
  b : All_fold P Γ
  p : P Γ d
  ============================
   ({| pr1 := []; pr2 := b0 |} =
    {| pr1 := d :: Γ; pr2 := All_fold_cons P b p |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  d0 : A
  Γ0 : list A
  b : All_fold P Γ0
  p0 : P Γ0 d0
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} =
    {| pr1 := d0 :: Γ0; pr2 := All_fold_cons P b p0 |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  P : list A → A → Type  b0 : All_fold P []
  ============================
   ({| pr1 := []; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  b0 : All_fold P []
  d : A
  Γ : list A
  b : All_fold P Γ
  p : P Γ d
  ============================
   ({| pr1 := []; pr2 := b0 |} =
    {| pr1 := d :: Γ; pr2 := All_fold_cons P b p |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} = {| pr1 := []; pr2 := All_fold_nil P |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)

  
  A : Type
  P : list A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  b0 : All_fold P (d :: Γ)
  d0 : A
  Γ0 : list A
  b : All_fold P Γ0
  p0 : P Γ0 d0
  ============================
   ({| pr1 := d :: Γ; pr2 := b0 |} =
    {| pr1 := d0 :: Γ0; pr2 := All_fold_cons P b p0 |}
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P (d :: Γ) (All_fold_cons P a p) b0
      → let H0 := CoreTactics.block in All_fold_cons P a p = b0)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim