Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  Γ' : list A
  d' : A
  ============================
   (All2_fold P Γ Γ'
    → nth_error Γ' n = Some d'
      → ∑ d : A,
          nth_error Γ n = Some d
          × (let Γs := skipn (S n) Γ in
             let Γs' := skipn (S n) Γ' in All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
induction n in Γ, Γ', d' |- *

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  d' : A
  ============================
   (All2_fold P Γ Γ'
    → nth_error Γ' 0 = Some d'
      → ∑ d : A,
          nth_error Γ 0 = Some d
          × (let Γs := skipn 1 Γ in
             let Γs' := skipn 1 Γ' in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  ============================
   (All2_fold P Γ Γ'
    → nth_error Γ' (S n) = Some d'
      → ∑ d : A,
          nth_error Γ (S n) = Some d
          × (let Γs := skipn (S (S n)) Γ in
             let Γs' := skipn (S (S n)) Γ' in
             All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
destruct Γ'
DEBUG LTAC Evaluated term: n

Goals:
    A : Type  P : list A → list A → A → A → Type  Γ : list A  d' : A
  ============================
   (All2_fold P Γ []
    → nth_error [] 0 = Some d'
      → ∑ d : A,
          nth_error Γ 0 = Some d
          × (let Γs := skipn 1 Γ in
             let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  ============================
   (All2_fold P Γ (a :: Γ')
    → nth_error (a :: Γ') 0 = Some d'
      → ∑ d : A,
          nth_error Γ 0 = Some d
          × (let Γs := skipn 1 Γ in
             let Γs' := skipn 1 (a :: Γ') in
             All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  ============================
   (All2_fold P Γ []
    → nth_error [] (S n) = Some d'
      → ∑ d : A,
          nth_error Γ (S n) = Some d
          × (let Γs := skipn (S (S n)) Γ in
             let Γs' := skipn (S (S n)) [] in
             All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  ============================
   (All2_fold P Γ (a :: Γ')
    → nth_error (a :: Γ') (S n) = Some d'
      → ∑ d : A,
          nth_error Γ (S n) = Some d
          × (let Γs := skipn (S (S n)) Γ in
             let Γs' := skipn (S (S n)) (a :: Γ') in
             All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
intros Hrel H
DEBUG LTAC Evaluated term: Γ'
DEBUG LTAC Evaluated term: Γ'

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
noconf H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
fun H => DepElim.noconf H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
DepElim.noconf H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
fun H =>
             CoreTactics.block_goal; CoreTactics.revert_until H;
              CoreTactics.block_goal;
              CoreTactics.on_last_hyp ltac:(fun H' => revert H');
              DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
              CoreTactics.intros_until_block

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal; CoreTactics.revert_until H;
            CoreTactics.block_goal;
            CoreTactics.on_last_hyp ltac:(fun H' => revert H');
            DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
            CoreTactics.intros_until_block

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal; CoreTactics.revert_until H;
            CoreTactics.block_goal;
            CoreTactics.on_last_hyp ltac:(fun H' => revert H');
            DepElim.simplify_dep_elim; CoreTactics.intros_until_block
Level 2: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
CoreTactics.block_goal; CoreTactics.revert_until H; CoreTactics.block_goal;
 CoreTactics.on_last_hyp ltac:(fun H' => revert H');
 DepElim.simplify_dep_elim; CoreTactics.intros_until_block;
 CoreTactics.intros_until_block
where
H := H
of type
ident of type tacvalue


Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal; CoreTactics.revert_until H;
            CoreTactics.block_goal;
            CoreTactics.on_last_hyp ltac:(fun H' => revert H');
            DepElim.simplify_dep_elim

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal; CoreTactics.revert_until H;
            CoreTactics.block_goal;
            CoreTactics.on_last_hyp ltac:(fun H' => revert H')

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal; CoreTactics.revert_until H;
            CoreTactics.block_goal

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal; CoreTactics.revert_until H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
CoreTactics.block_goal

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  d' : A
  Hrel : All2_fold P Γ []
  H : nth_error [] 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') 0 = Some d'
  ============================
   (∑ d : A,
      nth_error Γ 0 = Some d
      × (let Γs := skipn 1 Γ in
         let Γs' := skipn 1 (a :: Γ') in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ []
  H : nth_error [] (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) [] in All2_fold P Γs Γs' × P Γs Γs' d d'))

  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : A
  Γ' : list A
  d' : A
  IHn : ∀ (Γ Γ' : list A) (d' : A),
          All2_fold P Γ Γ'
          → nth_error Γ' n = Some d'
            → ∑ d : A,
                nth_error Γ n = Some d
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P Γ (a :: Γ')
  H : nth_error (a :: Γ') (S n) = Some d'
  ============================
   (∑ d : A,
      nth_error Γ (S n) = Some d
      × (let Γs := skipn (S (S n)) Γ in
         let Γs' := skipn (S (S n)) (a :: Γ') in
         All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
match goal with
           | |- ?T => change (let _ := CoreTactics.block in T)
           end