prop_neg a = a + a == 0

prop_neg a = a - a == 0

prop_inv :: Nimber -> Bool
prop_inv a = a == 0 || recip (recip a) == a

main = check prop_neg >> check prop_assoc_add >> check prop_assoc_mul >> check prop_distrib >> check prop_recip

main = check prop_neg >> check prop_assoc_add >> check prop_assoc_mul >> check prop_distrib >> check prop_recip >> check prop_inv