Goal:
  
  ============================
   (∀ (A B C : Type) (Q : C → Type) (P : C → A → Prop),
      (∀ x : A, (∀ y : C, Q y → P y x) → B)
      → (∀ l : list A, (∀ y : C, Q y → ∥ All (P y) l ∥) → list B)
        → ∀ (x : A) (xs : list A),
            (∀ y : C, Q y → ∥ All (P y) (x :: xs) ∥)
            → ∀ y : C, Q y → ∥ All (P y) xs ∥)


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