  Finding the set of leaves for an unbounded tree is a nontrivial process in
both the Weihrauch and reverse mathematics settings. Despite this, many
combinatorial principles for trees are equivalent to their restrictions to
trees with leaf sets. For example, let ${\widehat{\sf{WF}}}$ denote the problem
of choosing which trees in a sequence are well-founded, and let ${{\sf{PK}}}$
denote the problem of finding the perfect kernel of a tree. Let
${\widehat{\sf{WF}}}_L$ and ${{\sf{PK}}}_L$ denote the restrictions of these
principles to trees with leaf sets. Then ${\widehat{\sf{WF}}}$,
${\widehat{\sf{WF}}}_L$, ${{\sf{PK}}}$, and ${{\sf{PK}}}_L$ are all equivalent
to ${\Pi^1_1 {\rm -} {\sf{CA}}_0}$ over ${{\sf{RCA}}_0}$, and all strongly
Weihrauch equivalent.
