let A be non empty set ; :: thesis: for g, f being Element of Funcs A,REAL holds (minfuncreal A) . ((maxfuncreal A) . g,f),f = f
let g, f be Element of Funcs A,REAL ; :: thesis: (minfuncreal A) . ((maxfuncreal A) . g,f),f = f
thus (minfuncreal A) . ((maxfuncreal A) . g,f),f = (minfuncreal A) . f,((maxfuncreal A) . g,f) by Th21
.= f by Th29 ; :: thesis: verum