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:
match goal with
           | |- context [ eq_rect_r _ _ eq_refl ] => progress simpl eq_rect_r
           | |- context [ eq_rect _ _ _ _ eq_refl ] => progress simpl eq_rect
           | |- context [ Prop.Logic.transport _ eq_refl _ ] =>
                 progress simpl Prop.Logic.transport
           | |- context [ Logic.eq_elim _ _ _ _ _ eq_refl ] =>
                 progress simpl eq_rect
           | |- context [ Logic.eq_elim_r _ _ _ _ eq_refl ] =>
                 progress simpl Logic.eq_elim_r
           | |- context [ noConfusion_inv _ ] =>
                 progress simpl noConfusion_inv
           | |- DepElim.opaque_ind_pack_eq_inv ?G eq_refl =>
                 apply (DepElim.simplify_ind_pack_inv B x p G)
           | |- let _ := CoreTactics.block in _ => fail 1
           | |- _ => simplify * || simplify ?; cbv beta
           | |- _ → ?B =>
                 let ty := type of B in
                 intro || (let H := fresh in
                           intro
                           H)
           | |- ∀ x, _ => let H := fresh x in
                          intro
                          H
           | |- _ => intro
           end