Goal:
  
  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')
  Hrel0 := {| pr1 := {| pr1 := Γ; pr2 := a :: Γ' |}; pr2 := Hrel |}
        : sigma
            (λ index : sigma (λ _ : list A, list A),
               All2_fold P (pr1 index) (pr2 index))
  Hrel1 := {| pr1 := Γ; pr2 := a :: Γ' |} : sigma (λ _ : list A, list A)
  Hrel2 := Hrel
        : (λ index : sigma (λ _ : list A, list A),
             All2_fold P (pr1 index) (pr2 index)) Hrel1
  ============================
   ({| pr1 := Γ; pr2 := a :: Γ' |} = Hrel1
    → let H := CoreTactics.block in
      nth_error (a :: Γ') (S n) = Some d'
      → let H0 := CoreTactics.block in
        ∑ 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:
<coq-core.plugins.ltac::clearbody@0> $1