Goal:
  
  A : Type
  B : Type
  C : Type
  Q : C → Type
  P : C → A → Prop
  fn : ∀ x : A, (∀ y : C, Q y → P y x) → B
  x : A
  xs : list A
  h : ∀ y : C, Q y → ∥ All (P y) (x :: xs) ∥
  H : ∀ (n : nat) (x0 : A),
        nth_error xs n = Some x0
        → ∃ D : ∀ y : C, Q y → P y x0,
            nth_error (map_All fn xs (map_All_obligation_2 x xs h)) n =
            Some (fn x0 D)
  n : nat
  x0 : A
  H1 : nth_error (x :: xs) (S n) = Some x0
  ============================
   (∃ D : ∀ y : C, Q y → P y x0,
      nth_error (map_All fn (x :: xs) h) (S n) = Some (fn x0 D))


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H