reserve x,y for set;
reserve C,C9,D,D9,E for non empty set;
reserve c for Element of C;
reserve c9 for Element of C9;
reserve d,d1,d2,d3,d4,e for Element of D;
reserve d9 for Element of D9;

theorem Th1:
  for f being Function holds <:{},f:> = {} & <:f,{}:> = {}
proof
  let f be Function;
  dom <:{},f:> = dom {} /\ dom f & dom <:f,{}:> = dom f /\ dom {} by
FUNCT_3:def 7;
  hence thesis;
end;
