Section before_func.
Variable A : Type.
Variables f g : A -> bool.
Definition before_func_dec : forall l, {before_func f g l} + {~ before_func f g l}.
intros; induction l; simpl in *.
- intuition.
- destruct (f a); destruct (g a); intuition.
Defined.

Lemma before_func_app :
forall l x,
before_func f g l ->
before_func f g (l ++ x).