let A be non empty set ; :: thesis: for f, g being Element of Funcs A,REAL holds (minfuncreal A) . ((maxfuncreal A) . f,g),f = f
let f, g be Element of Funcs A,REAL ; :: thesis: (minfuncreal A) . ((maxfuncreal A) . f,g),f = f
thus (minfuncreal A) . ((maxfuncreal A) . f,g),f = (minfuncreal A) . ((maxfuncreal A) . g,f),f by Th20
.= f by Th30 ; :: thesis: verum