reserve x,y,z,r,s for ExtReal;
reserve A,B for ext-real-membered set;
reserve A,B for ext-real-membered set;

theorem
  for A being non empty Subset of ExtREAL st
   for r being Element of ExtREAL st r in A
  holds r <= -infty holds A = {-infty}
proof
  let A be non empty Subset of ExtREAL such that
A1: for r being Element of ExtREAL st r in A holds r <= -infty;
  assume A <> {-infty};
  then ex a being Element of A st a <> -infty by SETFAM_1:49;
  hence contradiction by A1,XXREAL_0:6;
end;
