Notation member := (in_dec eq_nat_dec).

Lemma pigeon : forall (l : list A) sub1 sub2, (forall a, In a sub1 -> In a l) -> (forall a, In a sub2 -> In a l) -> NoDup l -> NoDup sub1 -> NoDup sub2 -> length sub1 + length sub2 > length l -> exists a, In a sub1 /\ In a sub2.