let D, D9, E be non empty set ; :: thesis: for d being Element of D

for F being Function of [:D,D9:],E

for T9 being Tuple of 0 ,D9 holds F [;] (d,T9) = <*> E

let d be Element of D; :: thesis: for F being Function of [:D,D9:],E

for T9 being Tuple of 0 ,D9 holds F [;] (d,T9) = <*> E

let F be Function of [:D,D9:],E; :: thesis: for T9 being Tuple of 0 ,D9 holds F [;] (d,T9) = <*> E

let T9 be Tuple of 0 ,D9; :: thesis: F [;] (d,T9) = <*> E

T9 = <*> D9 ;

hence F [;] (d,T9) = <*> E by FINSEQ_2:79; :: thesis: verum

for F being Function of [:D,D9:],E

for T9 being Tuple of 0 ,D9 holds F [;] (d,T9) = <*> E

let d be Element of D; :: thesis: for F being Function of [:D,D9:],E

for T9 being Tuple of 0 ,D9 holds F [;] (d,T9) = <*> E

let F be Function of [:D,D9:],E; :: thesis: for T9 being Tuple of 0 ,D9 holds F [;] (d,T9) = <*> E

let T9 be Tuple of 0 ,D9; :: thesis: F [;] (d,T9) = <*> E

T9 = <*> D9 ;

hence F [;] (d,T9) = <*> E by FINSEQ_2:79; :: thesis: verum