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 p being PartState of S st IC S in dom p
  holds p +* Start-At(IC p,S) = p by FUNCT_4:7,98;
