let A be non empty 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

now

let x be Element of A; :: thesis: ((RealFuncMult A) . f,g) . x = ((RealFuncMult A) . g,f) . x
thus ((RealFuncMult A) . f,g) . x = (g . x) * (f . x) by Th11
.= ((RealFuncMult A) . g,f) . x by Th11 ; :: thesis: verum

end;

hence (RealFuncMult A) . f,g = (RealFuncMult A) . g,f by FUNCT_2:113; :: thesis: verum