F = (
    (set(['A']), set(['D'])),
    (set(['A','B']), set(['E'])),
    (set(['B','I']), set(['E'])),
    (set(['C','D']), set(['I'])),
    (set(['E']), set(['C'])),
)

$$AE^+$$

res = set(['A','E'])
mark = [0] * len(F)
while 1:
    pre_visted = sum(mark)
    for i in range(len(F)):
        if mark[i] == 0: # not visited
            if F[i][0].issubset(res):
                res = res.union(F[i][1])
                print(res)
                mark[i] = 1
    after_visted = sum(mark)
    if pre_visted == after_visted:
        break

{'A', 'E', 'D'}
{'C', 'A', 'E', 'D'}
{'I', 'C', 'A', 'E', 'D'}

F = (
    (set(['A','B']), set(['C'])),
    (set(['B']), set(['D'])),
    (set(['C','D']), set(['E'])),
    (set(['C','E']), set(['G','H'])),
    (set(['G']), set(['A'])),
)

$$F\mid= AB\rightarrow G$$

res = set(['A','B'])
mark = [0] * len(F)
while 1:
    pre_visted = sum(mark)
    for i in range(len(F)):
        if mark[i] == 0: # not visited
            if F[i][0].issubset(res):
                res = res.union(F[i][1])
                print(res)
                mark[i] = 1
    after_visted = sum(mark)
    if pre_visted == after_visted:
        break
'G' in res

{'B', 'C', 'A'}
{'B', 'C', 'A', 'D'}
{'B', 'C', 'A', 'E', 'D'}
{'H', 'G', 'B', 'C', 'A', 'E', 'D'}
{'H', 'G', 'B', 'C', 'A', 'E', 'D'}

True