Definition eq_bool_dec : forall a b : bool, {a = b} + {a <> b}.Fixpoint le_bool (a b : nat) {struct b} : bool :=
  match a, b with
  | O, _ => true
  | S a1, S b1 => le_bool a1 b1
  | _, _ => false
  end.

Theorem fold_left_eta : forall l a f1, (forall a b, In b l -> f a b = f1 a b) -> fold_left f l a = fold_left f1 l a.