let D, D9, E be non empty set ; :: thesis: for d being Element of D
for F being Function of [:D,D9:],E holds F [;] (d,(<*> D9)) = <*> E
let d be Element of D; :: thesis: for F being Function of [:D,D9:],E holds F [;] (d,(<*> D9)) = <*> E
let F be Function of [:D,D9:],E; :: thesis: F [;] (d,(<*> D9)) = <*> E
reconsider r = F [;] (d,(<*> D9)) as FinSequence of E by Th75;
len (<*> D9) = 0 ;
then len r = 0 by Th76;
hence F [;] (d,(<*> D9)) = <*> E ; :: thesis: verum