theorem :: MEMSTR_0:34

for N being with_zero set
for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for s1, s2 being State of S st s1 | ((Data-Locations ) \/ {(IC )}) = s2 | ((Data-Locations ) \/ {(IC )}) holds
s1 = s2