Goal:
  
  A : Type
  B : Type
  x : A
  xs : list A
  f0 : A → B
  H : ∀ (H := CoreTactics.block) (A0 B0 : Type) (f : A0 → B0) 
        (l : list A0) (g : ∀ x : A0, In x l → B0),
        g = (λ (x : A0) (_ : In x l), f x)
        → ∀ eqargs : {|
                       pr1 := A;
                       pr2 :=
                         {|
                           pr1 := B;
                           pr2 :=
                             {|
                               pr1 := xs;
                               pr2 := λ (x : A) (_ : In x xs), f0 x
                             |}
                         |}
                     |} =
                     {|
                       pr1 := A0;
                       pr2 :=
                         {| pr1 := B0; pr2 := {| pr1 := l; pr2 := g |} |}
                     |},
            eq_rect
              {|
                pr1 := A;
                pr2 :=
                  {|
                    pr1 := B;
                    pr2 :=
                      {| pr1 := xs; pr2 := λ (x : A) (_ : In x xs), f0 x |}
                  |}
              |}
              (λ projs : sigma
                           (λ A : Type,
                              sigma
                                (λ B : Type,
                                   sigma
                                     (λ l0 : list A, ∀ x : A, In x l0 → B))),
                 list (pr1 (pr2 projs)))
              (map_In xs (λ (x : A) (_ : In x xs), f0 x))
              {|
                pr1 := A0;
                pr2 := {| pr1 := B0; pr2 := {| pr1 := l; pr2 := g |} |}
              |} eqargs = map_In l g
            → let H0 := CoreTactics.block in map_In l g = map f l
  ============================
   (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:
cbn beta in hyp; eqns_specialize_eqs_block hyp;
            cbn[eq_rect_r eq_rect] in hyp