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 p being non empty PartState of S
 holds dom p meets {IC S} \/ Data-Locations S
  proof let S being IC-Ins-separated non empty
       with_non-empty_values Mem-Struct over N;
  let p being non empty PartState of S;
   dom p c= the carrier of S by RELAT_1:def 18;
   then dom p meets the carrier of S by XBOOLE_1:69;
   hence dom p meets {IC S} \/ Data-Locations S by STRUCT_0:4;
  end;
