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 x,y,z being object holds
  1 in dom <*x,y,z*> & 2 in dom <*x,y,z*> & 3 in dom <*x,y,z*>
proof
  let x,y,z be object;
  len <*x,y,z*> = 3 by Th45; then
  dom <*x,y,z*> = Seg 3 by Def3;
  hence thesis;
end;
