reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;

theorem Th27:
  the_set_of_all_right_open_real_bounded_intervals c=
    { I where I is Subset of REAL: I is right_open_interval}
  proof
    let x be object;
    assume x in the_set_of_all_right_open_real_bounded_intervals;
    then consider a,b be Real such that
A1: x = [.a,b.[;
    reconsider x1=x as Subset of REAL by A1;
    reconsider b as R_eal by XREAL_0:def 1,NUMBERS:31;
    x1 = [.a,b.[ by A1;
    then x1 is right_open_interval by MEASURE5:def 4;
    hence thesis;
  end;
