Goal:
  
  A : Type
  P : list A → A → Type
  a : A
  Γ : list A
  Δ : list A
  IHΓ : ∀ Δ : list A,
          All_fold P (Γ ++ Δ)
          → All_fold P Δ × All_fold (λ Γ : list A, P (Γ ++ Δ)) Γ
  X : All_fold P (a :: Γ ++ Δ)
  X0 := {| pr1 := a :: Γ ++ Δ; pr2 := X |}
     : sigma (λ index : list A, All_fold P index)
  X1 := a :: Γ ++ Δ : list A
  X2 := X : (λ index : list A, All_fold P index) X1
  ============================
   (a :: Γ ++ Δ = X1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All_fold (λ Γ : list A, P (Γ ++ Δ)) (a :: Γ))


DEBUG:Going to execute:
<coq-core.plugins.ltac::clearbody@0> $1