Definition l1 := 1.Definition l2 := 2.Definition f args :=
  match args with
  | x::y::_ => Some (x + y)
  | _ => None
  end.Definition prec (args : input) :=
  if args is x::y::_ then true else false.

Lemma prec_valid : forall i, prec i -> exists v, f i = Some v.