Goal:
  
  A : Type
  B : Type
  x : A
  xs : list A
  f0 : A → B
  H : (λ (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (f0 : A → B) (l0 : list A) 
           (g : ∀ x0 : A, In x0 l0 → B),
           g = (λ (x0 : A) (_ : In x0 l0), f0 x0)
           → {| pr1 := l; pr2 := f |} = {| pr1 := l0; pr2 := g |}
             → x = map_InP l0 g
               → let H0 := CoreTactics.block in map_InP l0 g = map f0 l0) xs
        (λ (x0 : A) (inx : In x0 xs),
           (λ (x1 : A) (_ : In x1 (x :: xs)), f0 x1) x0
             (map_InP_obligations_obligation_2 x xs x0 inx))
        (map_InP xs
           (λ (x0 : A) (inx : In x0 xs),
              (λ (x1 : A) (_ : In x1 (x :: xs)), f0 x1) x0
                (map_InP_obligations_obligation_2 x xs x0 inx)))
  ============================
   (let H := CoreTactics.block in
    map_InP (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f0 x0) =
    map f0 (x :: xs))


DEBUG:Going to execute:
match goal with
           | |- context [ eq_rect_r _ _ eq_refl ] => progress simpl eq_rect_r
           | |- context [ eq_rect _ _ _ _ eq_refl ] => 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