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
  X1 : list A
  X : All_fold P X1
  ============================
   (a :: Γ ++ Δ = X1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All_fold P Δ)


DEBUG:Going to execute:
match type of id with
           | sigma _ =>
               let xn := fresh id "'" in
               destruct id as [xn id]; DepElim.decompose_exists xn id;
                cbv beta iota delta [TODO projection TODO projection]
                 in id, id'; DepElim.decompose_exists id id'
           | _ =>
               cbv beta iota delta [TODO projection TODO projection]
                in id, id'
           end