reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem Th130:
  r <= s implies [.r,s.] = {r} \/ ].r,s.]
proof
  assume
A1: r <= s;
  let t;
  thus t in [.r,s.] implies t in {r} \/ ].r,s.]
  proof
    assume t in [.r,s.];
    then t in ].r,s.] or t = r by Th6;
    then t in ].r,s.] or t in {r} by TARSKI:def 1;
    hence thesis by XBOOLE_0:def 3;
  end;
  assume t in {r} \/].r,s.];
  then t in ].r,s.] or t in {r} by XBOOLE_0:def 3;
  then t in ].r,s.] or t = r by TARSKI:def 1;
  hence thesis by A1,Th1,Th12;
end;
