Goal:
  
  A : Type
  P : nat → A → Type
  n : nat
  hd : A
  tl : list A
  p : P n hd
  X : Alli P (S n) tl
  IHX : All_fold (λ (Γ : list A) (d : A), P (S n + #|Γ|) d) (List.rev tl)
  ============================
   (P n hd)


DEBUG:Going to execute:
let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction
           | congruence ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); try arith_congr;
             (solve [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"