let x, y be ExtReal; :: thesis: y is UpperBound of ].x,y.]
let z be ExtReal; :: according to XXREAL_2:def 1 :: thesis: ( z in ].x,y.] implies z <= y )
assume z in ].x,y.] ; :: thesis: z <= y
hence z <= y by XXREAL_1:2; :: thesis: verum