Goal:
  
  A : Type
  P : list A → A → Type
  b0 : All_fold P []
  b : sigma (λ index : list A, All_fold P index)
  ============================
   ({| pr1 := []; pr2 := b0 |} = b
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All_fold A P []
                                        (All_fold_nil P) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All_fold_obligation_2 A P [] 
          (All_fold_nil P) b0
          (noConfusionHom_All_fold_obligation_1 A P [] (All_fold_nil P) b0 e) =
        e)


DEBUG:Going to execute:
fun id id' =>
             hnf in id;
              match type of id with
              | sigma _ =>
                  let xn := fresh id "'" in
                  destruct id as [xn id]; DepElim.decompose_exists xn id;
                   cbv beta iota delta [TODO projection TODO projection]
                    in id, id'; DepElim.decompose_exists id id'
              | _ =>
                  cbv beta iota delta [TODO projection TODO projection]
                   in id, id'
              end