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 C1,C2 are_similar_wrt f,g holds
for s1 being State of C1
for s2 being State of C2 st s1 = s2 * f holds
for n being Element of NAT holds Following (s1,n) = (Following (s2,n)) * f by Th47, Th53;