theorem
 for f being Function st f in D* & x in dom f holds f.x in D
proof let f be Function such that
A1: f in D* and
A2: x in dom f;
  f is FinSequence of D by A1,Def11;
  then rng f c= D by Def4;
  hence f.x in D by A2,FUNCT_1:3;
end;
