reserve k for Element of NAT;
reserve r,r1 for Real;
reserve i for Integer;
reserve q for Rational;

theorem Th13:
  for a being R_eal st for r being Real holds a < r
     holds a = -infty
proof
  let a being R_eal;
  assume
A1: for r being Real holds a < r;
  assume
A2: not a = -infty;
 -infty <= a by XXREAL_0:5;
then  -infty < a by A2,XXREAL_0:1;
  then consider b being R_eal such that
  -infty < b and
A3: b < a and
A4: b in REAL by MEASURE5:2;
  reconsider b as Real by A4;
  b <= a by A3;
  hence contradiction by A1;
end;
