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 Th23:
  for d being data-only PartState of S, k being Nat
  holds d tolerates Start-At(k,S)
proof
  let d be data-only PartState of S, k be Nat;
  dom d misses dom Start-At(k,S) by Th10,ZFMISC_1:50;
  hence thesis by PARTFUN1:56;
end;
