
theorem Th5:
  for a,b being R_eal st a <= b holds a = -infty & b = -infty or a
  = -infty & b in REAL or a = -infty & b = +infty or a in REAL & b in REAL or a
  in REAL & b = +infty or a = +infty & b = +infty
proof
  let a,b be R_eal;
  a in REAL or a in {-infty,+infty} by XBOOLE_0:def 3,XXREAL_0:def 4;
  then
A1: a in REAL or a = -infty or a = +infty by TARSKI:def 2;
  b in REAL or b in {-infty,+infty} by XBOOLE_0:def 3,XXREAL_0:def 4;
  then
A2: b in REAL or b = -infty or b = +infty by TARSKI:def 2;
  assume a <= b;
  hence thesis by A1,A2,XXREAL_0:9,12;
end;
