let A be set ; 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); (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
; verum