def get(matches, used, Ps, get_P, Pa, ua):
others = list(set(used) - set(matches))
extra = PosetProduct(tuple(map(get_P, others)))
print('extra for Pa: %s' % extra)
Pa_comp = PosetProduct(Pa.subs + extra.subs)
print('Pa_comp: %s' % Pa_comp)
extra_minimals = extra.get_minimal_elements()
m_matches = matches + others
s = set()
R = set()
for m1, m2 in itertools.product(ua.minimals, extra_minimals):
m = m1 + m2
s.add(m)
r = [None] * len(used)
for i, a in enumerate(used):
S1 = Pa_comp.subs[m_matches.index(a)]
s1 = m[m_matches.index(a)]
S2 = get_P(a)
r[i] = express_value_in_isomorphic_space(S1, s1, S2)
r = tuple(r)
R.add(r)
Pa_comp_lb = Pa_comp.Us(s)
print('Pa_comp_lb: %s' % Pa_comp_lb)
Ps_a = Ps.Us(R)
return Ps_a
