let D, D9, E be non empty set ; for d being Element of D
for i being natural Number
for F being Function of [:D,D9:],E
for T9 being Tuple of i,D9 holds F [;] (d,T9) = (F [;] (d,(id D9))) * T9
let d be Element of D; for i being natural Number
for F being Function of [:D,D9:],E
for T9 being Tuple of i,D9 holds F [;] (d,T9) = (F [;] (d,(id D9))) * T9
let i be natural Number ; for F being Function of [:D,D9:],E
for T9 being Tuple of i,D9 holds F [;] (d,T9) = (F [;] (d,(id D9))) * T9
let F be Function of [:D,D9:],E; for T9 being Tuple of i,D9 holds F [;] (d,T9) = (F [;] (d,(id D9))) * T9
let T9 be Tuple of i,D9; F [;] (d,T9) = (F [;] (d,(id D9))) * T9
rng T9 c= D9
;
hence F [;] (d,T9) =
F [;] (d,((id D9) * T9))
by RELAT_1:53
.=
(F [;] (d,(id D9))) * T9
by FUNCOP_1:34
;
verum