let A be non empty set ; :: thesis: for f, g, h being Element of Funcs (A,COMPLEX) holds (ComplexFuncMult A) . (f,((ComplexFuncMult A) . (g,h))) = (ComplexFuncMult A) . (((ComplexFuncMult A) . (f,g)),h)
let f, g, h be Element of Funcs (A,COMPLEX); :: thesis: (ComplexFuncMult A) . (f,((ComplexFuncMult A) . (g,h))) = (ComplexFuncMult A) . (((ComplexFuncMult A) . (f,g)),h)

now :: thesis: for x being Element of A holds ((ComplexFuncMult A) . (f,((ComplexFuncMult A) . (g,h)))) . x = ((ComplexFuncMult A) . (((ComplexFuncMult A) . (f,g)),h)) . x

let x be Element of A; :: thesis: ((ComplexFuncMult A) . (f,((ComplexFuncMult A) . (g,h)))) . x = ((ComplexFuncMult A) . (((ComplexFuncMult A) . (f,g)),h)) . x
thus ((ComplexFuncMult A) . (f,((ComplexFuncMult A) . (g,h)))) . x = (f . x) * (((ComplexFuncMult A) . (g,h)) . x) by Th2
.= (f . x) * ((g . x) * (h . x)) by Th2
.= ((f . x) * (g . x)) * (h . x)
.= (((ComplexFuncMult A) . (f,g)) . x) * (h . x) by Th2
.= ((ComplexFuncMult A) . (((ComplexFuncMult A) . (f,g)),h)) . x by Th2 ; :: thesis: verum

end;

hence (ComplexFuncMult A) . (f,((ComplexFuncMult A) . (g,h))) = (ComplexFuncMult A) . (((ComplexFuncMult A) . (f,g)),h) by FUNCT_2:63; :: thesis: verum