def test_the_nature_of_bivalence_README_example():
lnc = Proposition('''¬(p & ¬p)''')
lem = Proposition('''(p v ¬p)''')
the_nature_of_bivalence = Proposition('{} <-> {}'.format(lnc, lem))
assert the_nature_of_bivalence.is_theorem() == True
def test_implication_distribution_via_direct_truth_table():
prop = Proposition('''(p -> (q -> r)) <-> ((p -> q) -> (p -> r))''')
assert prop.is_theorem() == True
def test_absorption_via_direct_truth_table():
prop = Proposition('''(p -> q) <-> (p -> (p & q))''')
assert prop.is_theorem() == True
def test_contraposition_via_direct_truth_table():
prop = Proposition('''(p -> q) <-> (~q -> ~p)''')
assert prop.is_theorem() == True