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

theorem Th131:
  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 Th8;
    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,Th3,Th14;
end;
