let D, D9, E be non empty set ; :: thesis: for d9 being Element of D9
for F being Function of [:D,D9:],E holds F [:] ((<*> D),d9) = <*> E
let d9 be Element of D9; :: 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 Th81;
len (<*> D) = 0 ;
then len r = 0 by Th82;
hence F [:] ((<*> D),d9) = <*> E ; :: thesis: verum