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
    → let H := CoreTactics.block in
      NoConfusionHom_All_fold A P [] (All_fold_nil P) b0
      → let H0 := CoreTactics.block in All_fold_nil P = b0)


DEBUG:Going to execute:
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'