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
  the_set_of_all_left_open_real_bounded_intervals c=
    { I where I is Subset of REAL: I is left_open_interval}
  proof
    let x be object;
    assume x in the_set_of_all_left_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 a as R_eal by XREAL_0:def 1,NUMBERS:31;
    x1 = ].a,b.] by A1;
    then x1 is left_open_interval by MEASURE5:def 5;
    hence thesis;
  end;
