reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;
reserve a, b, c, d, e, f for object;

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;
