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;
