theorem :: AOFA_L00:31

for U1, U2 being Universal_Algebra st UAStr(# the carrier of U1, the charact of U1 #) = UAStr(# the carrier of U2, the charact of U2 #) holds
for S1 being Subset of U1
for S2 being Subset of U2 st S1 = S2 holds
for o1 being operation of U1
for o2 being operation of U2 st o1 = o2 & S1 is_closed_on o1 holds
S2 is_closed_on o2 ;