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