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 left_end non right_end interval ext-real-membered
  set ex r,s st r <= s & A =].r,s.[
proof
  let A be non left_end non right_end interval ext-real-membered set;
  per cases;
  suppose
A1: A is empty;
    take -infty,-infty;
    thus thesis by A1;
  end;
  suppose
A2: A is not empty;
    take inf A, sup A;
    thus inf A <= sup A by A2,Th40;
    thus thesis by A2,Th78;
  end;
end;
