Goal:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  R : C → A → Prop
  f : ∀ x : A, (∀ y : C, Q y → R y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (R y) (x :: xs) ∥
  X : ∀ (P : C → A → Prop) (Q' : B → Type),
        (∀ y : C, Q y → All (P y) xs)
        → (∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x),
             P y x → Q' (f x rx))
          → ∀ y : C,
              Q y → All Q' (map_All f xs (map_All_obligation_2 x xs h))
  P : C → A → Prop
  Q' : B → Type
  ha : ∀ y : C, Q y → All (P y) (x :: xs)
  hf : ∀ (x : A) (y : C) (rx : ∀ y0 : C, Q y0 → R y0 x), P y x → Q' (f x rx)
  y : C
  hy : Q y
  p : P y x
  X0 : All (P y) xs
  y0 : C
  p0 : P y0 x
  X1 : All (P y0) xs
  ============================
   (All (P y0) xs)


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"