Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  H1' : list A
  H1 : list A
  H : All2_fold Q H1' H1
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  d' : A
  Γ : list A
  Γ'0 : list A
  H : All2_fold Q Γ Γ'0
  q : Q Γ Γ'0 d d'
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := d :: Γ; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  d0 : A
  d' : A
  Γ0 : list A
  Γ'0 : list A
  H : All2_fold Q Γ0 Γ'0
  q : Q Γ0 Γ'0 d0 d'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := d0 :: Γ0; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  d' : A
  Γ : list A
  Γ'0 : list A
  H : All2_fold Q Γ Γ'0
  q : Q Γ Γ'0 d d'
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := d :: Γ; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  d0 : A
  d' : A
  Γ0 : list A
  Γ'0 : list A
  H : All2_fold Q Γ0 Γ'0
  q : Q Γ0 Γ'0 d0 d'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := d0 :: Γ0; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')


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

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  d' : A
  Γ : list A
  Γ'0 : list A
  H : All2_fold Q Γ Γ'0
  q : Q Γ Γ'0 d d'
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := d :: Γ; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  d0 : A
  d' : A
  Γ0 : list A
  Γ'0 : list A
  H : All2_fold Q Γ0 Γ'0
  q : Q Γ0 Γ'0 d0 d'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := d0 :: Γ0; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')


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

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  d' : A
  Γ : list A
  Γ'0 : list A
  H : All2_fold Q Γ Γ'0
  q : Q Γ Γ'0 d d'
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := d :: Γ; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  d0 : A
  d' : A
  Γ0 : list A
  Γ'0 : list A
  H : All2_fold Q Γ0 Γ'0
  q : Q Γ0 Γ'0 d0 d'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := d0 :: Γ0; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  d' : A
  Γ : list A
  Γ'0 : list A
  H : All2_fold Q Γ Γ'0
  q : Q Γ Γ'0 d d'
  ============================
   ({| pr1 := []; pr2 := Γ' |} = {| pr1 := d :: Γ; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') [] Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ' : list A
  d : A
  Γ : list A
  X : All_fold P Γ
  p : P Γ d
  IHX : ∀ Γ' : list A,
          All2_fold Q Γ Γ'
          → All2_fold (λ (Γ Γ'0 : list A) (d d' : A), P Γ d × Q Γ Γ'0 d d') Γ
              Γ'
  d0 : A
  d' : A
  Γ0 : list A
  Γ'0 : list A
  H : All2_fold Q Γ0 Γ'0
  q : Q Γ0 Γ'0 d0 d'
  ============================
   ({| pr1 := d :: Γ; pr2 := Γ' |} = {| pr1 := d0 :: Γ0; pr2 := d' :: Γ'0 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ d × Q Γ Γ' d d') 
        (d :: Γ) Γ')


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim