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) 
           (Hl0 : ∀ y : C, Q y → ∥ All (P y) l0 ∥),
           {| pr1 := l; pr2 := Hl |} = {| pr1 := l0; pr2 := Hl0 |}
           → x = map_All fn l0 Hl0
             → let H0 := CoreTactics.block in #|map_All fn l0 Hl0| = #|l0|)
        xs (map_All_obligation_2 x xs h)
        (map_All fn xs (map_All_obligation_2 x xs h))
  ============================
   (∀ (l : list A) (Hl : ∀ y : C, Q y → ∥ All (P y) l ∥),
      {| pr1 := x :: xs; pr2 := h |} = {| pr1 := l; pr2 := Hl |}
      → fn x (map_All_obligation_1 x xs h)
        :: map_All fn xs (map_All_obligation_2 x xs h) = 
        map_All fn l Hl
        → let H := CoreTactics.block in #|map_All fn l Hl| = #|l|)


DEBUG:Going to execute:
match goal with
           | |- context [ rew <- [_] eq_refl in _ ] =>
                 progress simpl eq_rect_r
           | |- context [ rew [_] eq_refl in _ ] => progress simpl eq_rect
           | |- context [ Prop.Logic.transport _ eq_refl _ ] =>
                 progress simpl Prop.Logic.transport
           | |- context [ Logic.eq_elim _ _ _ _ _ eq_refl ] =>
                 progress simpl eq_rect
           | |- context [ Logic.eq_elim_r _ _ _ _ eq_refl ] =>
                 progress simpl Logic.eq_elim_r
           | |- context [ noConfusion_inv _ ] =>
                 progress simpl noConfusion_inv
           | |- DepElim.opaque_ind_pack_eq_inv ?G eq_refl =>
                 apply (DepElim.simplify_ind_pack_inv B x p G)
           | |- let _ := CoreTactics.block in _ => fail 1
           | |- _ => simplify * || simplify ?; cbv beta
           | |- _ → ?B =>
                 let ty := type of B in
                 intro || (let H := fresh in
                           intro
                           H)
           | |- ∀ x, _ => let H := fresh x in
                          intro
                          H
           | |- _ => intro
           end