
theorem Th02:
  Family_of_halflines c= Family_of_Intervals
proof
   now let A be object;
    assume A in Family_of_halflines; then
    consider r be Element of REAL such that
A1:  A = halfline r by PROB_1:def 11;
    A = ].-infty,r.[ by A1,PROB_1:def 10;
    hence A in Family_of_Intervals by A1;
   end;
   hence thesis;
end;
