for G1, G2 being non empty non void Circuit-like ManySortedSign
for f, g being Function
for C1 being non-empty Circuit of G1
for C2 being non-empty Circuit of G2 st f,g form_embedding_of C1,C2 holds
for o1 being Gate of G1
for o2 being Gate of G2 st o2 = g . o1 holds
for s1 being State of C1
for s2 being State of C2 st s1 = s2 * f holds
o2 depends_on_in s2 = o1 depends_on_in s1