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

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