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 Th45:
 for p being PartState of S
  holds DataPart Initialize p = DataPart p
 proof let p be PartState of S;
  thus DataPart Initialize p
        = DataPart p +* DataPart Start-At(0,S) by FUNCT_4:71
       .= DataPart p +* {} by Th20
       .= DataPart p;
 end;
