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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th15</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: MODAL_1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Z</font> being   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a><br/>  for <font color="Olive" title="b2">o</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Olive" title="b1">Z</font>  st <font color="Olive" title="b2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K1" title="MODAL_1:func.1">Root</a> <font color="Olive" title="b1">Z</font> holds <br/>( <font color="Olive" title="b1">Z</font> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Olive" title="b2">o</font>,<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b2">o</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">s9</font></span>)</span> where <font color="Olive" title="b3">s9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  : <font color="Olive" title="b2">o</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">s9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Z</font> </span> } </span>  <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp;  not  <a href="modal_1.html#K1" title="MODAL_1:func.1">Root</a> <font color="Olive" title="b1">Z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b2">o</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">w9</font></span>)</span> where <font color="Olive" title="b3">w9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  : <font color="Olive" title="b2">o</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">w9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">Z</font> </span> } </span>  )</div></div>
