let A be set ; :: thesis: 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); :: thesis: (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 ; :: thesis: verum