Using your notations, what we assume is that .
You want to send a map from to on a map from to .
means there is a map such that is a bijection from into .
Prove that is an injection.
Show that if κ ≤ λ then κ^μ ≤ λ^μ for any cardinals μ, κ and λ .
I was thinking setting the sets A, B and C to be sets with cardinals κ, λ and μ respectively. Then I'd just need to prove that A^C ≤ B^C gives an injection. If someone could help out with a sketch of the proof that would be great.
(I think it's also helpful to note that A^B is defined to be the set of all functions from B to A and κ^λ = card(A^B), but I'm not sure how to apply these).