def no_proof_of(givens, conclusion):
"""Finds a formula that represents the givens not implying the conclusion."""
if wff(givens):
givens = (givens, )
else:
givens = tuple(givens)
return ~Implies(*(givens + (conclusion, )))
def iff(a, b):
"""Creates a formula for a implies b and b implies a."""
assert wff(a), a
assert wff(b), b
return a >> b & b >> a