Prove a set is well-ordered

Let $FS(?, ?) ? { f | f : ?->? & Fin( {? | ? ? ? & not( f(?) = 0 ) })}$ for all ordinals ?, ?,
where Fin(A) means the set A is finite.

We define a relation ? on FS:  $f ? g ?? (?? < ?)( f(?) < g(?) & (?? < ?)( ? < ? ? f(?) = g(?)))$.

How to prove that (FS, ?) is well-ordered?

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