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

theorem Th132:
  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 Th9;
    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,Th2,Th15;
end;
