Section CalculatorApp.
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.