reserve x,N for set,
        k for Nat;
reserve N for with_zero set;
reserve S for IC-Ins-separated non empty with_non-empty_values
     Mem-Struct over N;
reserve s for State of S;
reserve p for PartState of S;

theorem
 for S being IC-Ins-separated non empty with_non-empty_values
        Mem-Struct over N
 for s1,s2 be State of S
  st s1|(Data-Locations S \/ {IC S}) = s2|(Data-Locations S \/ {IC S})
 holds s1 =  s2
proof
 let S be IC-Ins-separated non empty with_non-empty_values Mem-Struct over N;
 let s1,s2 be State of S;
  s1 = s1|(Data-Locations S \/ {IC S}) by Th33;
 hence thesis by Th33;
end;
