let i be natural Number ; :: thesis: for D, D9, E being non empty set
for d being Element of D
for F being Function of [:D,D9:],E
for z being Tuple of i,D9 holds F [;] (d,z) is Element of i -tuples_on E
let D, D9, E be non empty set ; :: thesis: for d being Element of D
for F being Function of [:D,D9:],E
for z being Tuple of i,D9 holds F [;] (d,z) is Element of i -tuples_on E
let d be Element of D; :: thesis: for F being Function of [:D,D9:],E
for z being Tuple of i,D9 holds F [;] (d,z) is Element of i -tuples_on E
let F be Function of [:D,D9:],E; :: thesis: for z being Tuple of i,D9 holds F [;] (d,z) is Element of i -tuples_on E
let z be Tuple of i,D9; :: thesis: F [;] (d,z) is Element of i -tuples_on E
reconsider r = F [;] (d,z) as FinSequence of E by Th75;
len z = i by CARD_1:def 7;
then len r = i by Th76;
hence F [;] (d,z) is Element of i -tuples_on E by Th90; :: thesis: verum