theorem
  for TS being transition-system over F holds dom (the Tran of TS)
  = {} implies TS is deterministic
proof
  let TS be transition-system over F;
  assume dom (the Tran of TS) = {};
  then
  (the Tran of TS) = {} & for s being Element of TS, u, v st u <> v & [s,
u] in dom (the Tran of TS) & [s, v] in dom (the Tran of TS) holds not ex w st u
  ^w = v or v^w = u;
  hence thesis;
end;
