Goal:
  
  A : Type
  B : Type
  x : A
  xs : list A
  f0 : A → B
  H : (λ (A B : Type) (l : list A) (f : ∀ x : A, In x l → B) (x : list B),
         ∀ (H := CoreTactics.block) (A0 B0 : Type) 
           (f0 : A0 → B0) (l0 : list A0) (g : ∀ x0 : A0, In x0 l0 → B0),
           g = (λ (x0 : A0) (_ : In x0 l0), f0 x0)
           → ∀ eqargs : {|
                          pr1 := A;
                          pr2 :=
                            {| pr1 := B; pr2 := {| pr1 := l; pr2 := f |} |}
                        |} =
                        {|
                          pr1 := A0;
                          pr2 :=
                            {| pr1 := B0; pr2 := {| pr1 := l0; pr2 := g |} |}
                        |},
               eq_rect
                 {|
                   pr1 := A;
                   pr2 := {| pr1 := B; pr2 := {| pr1 := l; pr2 := f |} |}
                 |}
                 (λ projs : sigma
                              (λ A1 : Type,
                                 sigma
                                   (λ B1 : Type,
                                      sigma
                                        (λ l1 : list A1,
                                           ∀ x0 : A1, In x0 l1 → B1))),
                    list (pr1 (pr2 projs))) x
                 {|
                   pr1 := A0;
                   pr2 := {| pr1 := B0; pr2 := {| pr1 := l0; pr2 := g |} |}
                 |} eqargs = map_In l0 g
               → let H0 := CoreTactics.block in map_In l0 g = map f0 l0) A B
        xs
        (λ (x0 : A) (H : In x0 xs),
           (λ (x1 : A) (_ : In x1 (x :: xs)), f0 x1) x0
             (map_In_obligations_obligation_2 A x xs x0 H))
        (map_In xs
           (λ (x0 : A) (H : In x0 xs),
              (λ (x1 : A) (_ : In x1 (x :: xs)), f0 x1) x0
                (map_In_obligations_obligation_2 A x xs x0 H)))
  ============================
   (let H := CoreTactics.block in
    map_In (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f0 x0) =
    map f0 (x :: xs))


DEBUG:Going to execute:
cbv beta