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

theorem Th129:
  r <= s implies [.r,s.] = [.r,s.[ \/ {s}
proof
  assume
A1: r <= s;
  let t;
  thus t in [.r,s.] implies t in [.r,s.[ \/ {s}
  proof
    assume t in [.r,s.];
    then t in [.r,s.[ or t = s by Th7;
    then t in [.r,s.[ or t in {s} by TARSKI:def 1;
    hence thesis by XBOOLE_0:def 3;
  end;
  assume t in [.r,s.[ \/ {s};
  then t in [.r,s.[ or t in {s} by XBOOLE_0:def 3;
  then t in [.r,s.[ or t = s by TARSKI:def 1;
  hence thesis by A1,Th1,Th13;
end;
