Goal:
  
  A : Type
  B : Type
  f : ∀ x : A, In x [] → B
  A0 : Type
  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 := []; pr2 := f |} |}
                   |} =
                   {|
                     pr1 := A0;
                     pr2 := {| pr1 := B0; pr2 := {| pr1 := l; pr2 := g |} |}
                   |},
          eq_rect
            {|
              pr1 := A;
              pr2 := {| pr1 := B; pr2 := {| pr1 := []; 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))) []
            {|
              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 * || simplify ?; cbv beta