Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  d0 : A
  Γ0 : list A
  H : #|Γ| = #|Γ0|
  ha : All_fold P Γ
  p : P Γ d
  hb : All_fold P Γ0
  p0 : P Γ0 d0
  H0 : ∀ (Δ Δ' : list A) (x y : A),
         All_fold P Δ
         → All_fold P Δ' → All2_fold Q Δ Δ' → P Δ x → P Δ' y → Q Δ Δ' x y
  IHha : ∀ Δ : list A, #|Γ| = #|Δ| → All_fold P Δ → All2_fold Q Γ Δ
  ============================
   (All_fold P Γ0)


DEBUG:Going to execute:
let rec use_hyp H :=
            match type of H with
            | _ ∧ _ => exact H || destruct_hyp H
            | _ * _ => exact H || destruct_hyp H
            | _ => try (solve [ inversion H ])
            end
           with do_intro := let H := fresh in
                            intro H; use_hyp H
           with destruct_hyp H := case H; clear H; do_intro; do_intro
           in
           let rec use_hyps :=
            match goal with
            | H:_ ∧ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ * _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           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"