let A be set ; :: thesis: for f, g being Element of Funcs (A,REAL) holds (RealFuncAdd A) . (f,g) = (RealFuncAdd A) . (g,f)
let f, g be Element of Funcs (A,REAL); :: thesis: (RealFuncAdd A) . (f,g) = (RealFuncAdd A) . (g,f)
thus (RealFuncAdd A) . (f,g) = addreal .: (f,g) by Def1
.= addreal .: (g,f) by FUNCOP_1:65
.= (RealFuncAdd A) . (g,f) by Def1 ; :: thesis: verum