let A be set ; for f, g being Element of Funcs (A,REAL) holds (RealFuncMult A) . (f,g) = (RealFuncMult A) . (g,f)
let f, g be Element of Funcs (A,REAL); (RealFuncMult A) . (f,g) = (RealFuncMult A) . (g,f)
thus (RealFuncMult A) . (f,g) =
multreal .: (f,g)
by Def2
.=
multreal .: (g,f)
by FUNCOP_1:65
.=
(RealFuncMult A) . (g,f)
by Def2
; verum