let A be non empty set ; :: thesis: for f, g being Element of Funcs (A,REAL) holds (maxfuncreal A) . (((minfuncreal A) . (g,f)),f) = f
let f, g 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 Th9
.= f by Th13 ; :: thesis: verum