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 : (λ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥) (x : list B),
         ∀ (H := CoreTactics.block) (l0 : list A) 
           (H0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥) 
           (n : nat) (x0 : A),
           nth_error l0 n = Some x0
           → {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := H0 |}
             → x = map_All fn l0 H0
               → let H1 := CoreTactics.block in
                 ∃ D : ∀ y : C, Q y → P y x0,
                   nth_error (map_All fn l0 H0) n = Some (fn x0 D)) xs
        (map_All_obligation_2 x xs h)
        (map_All fn xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (l : list A) (H : ∀ y : C, Q y → ∥ All (P y) l ∥) (n : nat) (x0 : A),
      nth_error l n = Some x0
      → {| pr1 := x :: xs; pr2 := h |} = {| pr1 := l; pr2 := H |}
        → fn x (map_All_obligation_1 x xs h)
          :: map_All fn xs (map_All_obligation_2 x xs h) = 
          map_All fn l H
          → let H0 := CoreTactics.block in
            ∃ D : ∀ y : C, Q y → P y x0,
              nth_error (map_All fn l H) n = Some (fn x0 D))


DEBUG:Going to execute:
intro H