let A be set ; :: thesis: for f, g, h being Element of Funcs (A,REAL) holds (RealFuncMult A) . (f,((RealFuncMult A) . (g,h))) = (RealFuncMult A) . (((RealFuncMult A) . (f,g)),h)
let f, g, h be Element of Funcs (A,REAL); :: thesis: (RealFuncMult A) . (f,((RealFuncMult A) . (g,h))) = (RealFuncMult A) . (((RealFuncMult A) . (f,g)),h)
thus (RealFuncMult A) . (f,((RealFuncMult A) . (g,h))) = (RealFuncMult A) . (f,(multreal .: (g,h))) by Def3
.= multreal .: (f,(multreal .: (g,h))) by Def3
.= multreal .: ((multreal .: (f,g)),h) by FUNCOP_1:61
.= (RealFuncMult A) . ((multreal .: (f,g)),h) by Def3
.= (RealFuncMult A) . (((RealFuncMult A) . (f,g)),h) by Def3 ; :: thesis: verum