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:
cbv beta