Goal:
  
  A : Type
  P : nat → A → Type
  n : nat
  x : A
  Γ : list A
  IHΓ : All_fold (λ (Γ : list A) (d : A), P (n + #|Γ|) d) (List.rev Γ)
        → Alli P n Γ
  a1 : list A
  a : All_fold (λ (Γ : list A) (d : A), P (n + #|Γ|) d) a1
  ============================
   (x :: List.rev Γ = a1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in Alli P n (Γ ++ [x]))


DEBUG:Going to execute:
fun id id' =>
             hnf in id;
              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