Fact silly_fact_1 : forall m, foo m + 1 = foo (m + 1) + 1.
Admitted. (* QuickChick silly_fact_1. *)
Definition bar x :=
match x with
| O => 5
| S _ => 5
end.
Fact silly_fact_2 : forall m, bar m + 1 = bar (m + 1) + 1.
Admitted. (* QuickChick silly_fact_2. *)
Definition sillyfun (n : nat) : bool :=
if beq_nat n 3 then false
else if beq_nat n 5 then false
else false.

(* Specifications: *)
Theorem sillyfun_false : forall (n : nat),
sillyfun n = false.