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 Th8
.= f by Th18 ; :: thesis: verum