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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th18</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: MODAL_1:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">Z</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b3">z</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">Z</font>  st  <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <span class="p1">(<span class="default"><a href="modal_1.html#K1" title="MODAL_1:func.1">Root</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">Z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">z</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/><font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1</span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="modal_1.html#K2" title="MODAL_1:func.2">Root</a> <font color="Olive" title="b2">Z</font></span>)</span></span>)</span> <a href="trees_2.html#K7" title="TREES_2:func.7">with-replacement</a> (<span class="p1"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">Z</font> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Olive" title="b3">z</font></span>)</span>)</div></div>
