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 Th33:
 for S being IC-Ins-separated non empty with_non-empty_values
         Mem-Struct over N
 for s be State of S holds s = s|(Data-Locations S \/ {IC S})
proof
 let S be IC-Ins-separated non empty with_non-empty_values Mem-Struct over N;
 let s be State of S;
 thus  s = s|dom  s
     .= s|({IC S} \/ dom DataPart s) by Th2,Th24
     .= s|(Data-Locations S \/ {IC S}) by Th9;
end;
