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 Th27:
  IC S in dom (p +* Start-At( k,S))
proof
  IC S in dom Start-At( k,S) by TARSKI:def 1;
  hence thesis by FUNCT_4:12;
end;
