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

theorem
  ].s,+infty.[ = {g : s<g}
proof
  thus ].s,+infty.[ c= {g : s<g}
  proof
    let x be Real;
    assume
 x in ].s,+infty.[;
    then
A1: s < x by Th4;
    thus thesis by A1;
  end;
  let x be object;
  assume x in {g : s<g};
  then consider g such that
A2: x = g and
A3: s < g;
  g in REAL by XREAL_0:def 1;
  then g < +infty by XXREAL_0:9;
  hence thesis by A2,A3,Th4;
end;
