Goal:
  
  A : Type
  B : Type
  x : A
  xs : list A
  f : ∀ x0 : A, In x0 (x :: xs) → 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),
           f x0 (map_In_obligations_obligation_2 A x xs x0 H))
        (map_In xs
           (λ (x0 : A) (H : In x0 xs),
              f x0 (map_In_obligations_obligation_2 A x xs x0 H)))
  ============================
   (∀ (A0 B0 : Type) (f0 : A0 → B0) (l : list A0) (g : ∀ x : A0, In x l → B0),
      g = (λ (x : A0) (_ : In x l), f0 x)
      → ∀ eqargs : {|
                     pr1 := A;
                     pr2 :=
                       {| pr1 := B; pr2 := {| pr1 := x :: xs; pr2 := f |} |}
                   |} =
                   {|
                     pr1 := A0;
                     pr2 := {| pr1 := B0; pr2 := {| pr1 := l; pr2 := g |} |}
                   |},
          eq_rect
            {|
              pr1 := A;
              pr2 := {| pr1 := B; pr2 := {| pr1 := x :: xs; pr2 := f |} |}
            |}
            (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)))
            (f x (map_In_obligations_obligation_1 A x xs)
             :: map_In xs
                  (λ (x0 : A) (H : In x0 xs),
                     f x0 (map_In_obligations_obligation_2 A x xs x0 H)))
            {|
              pr1 := A0;
              pr2 := {| pr1 := B0; pr2 := {| pr1 := l; pr2 := g |} |}
            |} eqargs = map_In l g
          → let H := CoreTactics.block in map_In l g = map f0 l)


DEBUG:Going to execute:
simplify *