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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: TREES_9:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   <a href="trees_9.html#V1" title="TREES_9:attr.1">finite-branching</a>  <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a> holds <br/> ( <font color="Olive" title="b1">T</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  iff  ex <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b1">T</font> <a href="trees_2.html#K2" title="TREES_2:func.2">-level</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</div></div>
