let D, D9, E be non empty set ; :: thesis: 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; :: thesis: 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 ; :: thesis: 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; :: thesis: for T9 being Tuple of i,D9 holds F [;] (d,T9) = (F [;] (d,(id D9))) * T9
let T9 be Tuple of i,D9; :: thesis: 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 ;
:: thesis: verum