Goal:
  
  A : Type
  P : list A → A → Type
  l : list A
  a : All_fold P l
  b : All_fold P l
  H : a = b
  ============================
   (NoConfusionHom_All_fold A P l a b)


DEBUG:Going to execute:
match goal with
           | H:_ = _ |- _ = _ => try solve_noconf_hom_inv_equiv
           | H:_ = _ |- _ => try solve_noconf_prf
           | |- _ = _ => try solve_noconf_hom_inv
           end