Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h1' : list A
  h1 : list A
  h : All2_fold Q h1' h1
  ============================
   ({| pr1 := d :: Γ; pr2 := d' :: Γ' |} = {| pr1 := h1'; pr2 := h1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
destruct p

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

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

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

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


DEBUG:Going to execute:
DepElim.simpl_dep_elim

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

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

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

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


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

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

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

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

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


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

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

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

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

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


DEBUG:Going to execute:
DepElim.simplify_dep_elim

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

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

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

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


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim