let A be non empty set ; :: thesis: for g, f being Element of Funcs (A,REAL) holds (maxfuncreal A) . (((minfuncreal A) . (g,f)),f) = f
let g, f be Element of Funcs (A,REAL); :: thesis: (maxfuncreal A) . (((minfuncreal A) . (g,f)),f) = f
thus (maxfuncreal A) . (((minfuncreal A) . (g,f)),f) = (maxfuncreal A) . (((minfuncreal A) . (f,g)),f) by Th21
.= f by Th25 ; :: thesis: verum