take
].-infty ,+infty .[
; ( not ].-infty ,+infty .[ is empty & ].-infty ,+infty .[ is open_interval )
0 in ].-infty ,+infty .[
by XXREAL_1:224;
hence
not ].-infty ,+infty .[ is empty
; ].-infty ,+infty .[ is open_interval
take
-infty
; MEASURE5:def 5 ex b being R_eal st ].-infty ,+infty .[ = ].-infty ,b.[
take
+infty
; ].-infty ,+infty .[ = ].-infty ,+infty .[
thus
].-infty ,+infty .[ = ].-infty ,+infty .[
; verum