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

theorem Th35:
  x < y implies ].x,y.] is right_end
proof
  assume
A1: x < y;
  then y in ].x,y.] by XXREAL_1:2;
  hence sup ].x,y.] in ].x,y.] by A1,Th30;
end;
