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

theorem Th33:
  x <= y implies [.x,y.] is left_end right_end
proof
  assume
A1: x <= y;
  then x in [.x,y.] by XXREAL_1:1;
  then inf [.x,y.] in [.x,y.] by A1,Th25;
  hence [.x,y.] is left_end;
  y in [.x,y.] by A1,XXREAL_1:1;
  hence sup [.x,y.] in [.x,y.] by A1,Th29;
end;
