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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th19</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: MODAL_1:24</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">x1</font>, <font color="Olive" title="b3">x2</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">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> &amp; <font color="Olive" title="b3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default">1</span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span> &amp;  <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> <font color="Olive" title="b1">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> holds <br/><font color="Olive" title="b1">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> 2</span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<span class="p2"><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="p2">(<span class="default"><font color="Olive" title="b1">Z</font> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Olive" title="b2">x1</font></span>)</span>)</span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> (<span class="p1"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default">1</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="b1">Z</font> <a href="trees_1.html#K4" title="TREES_1:func.4">|</a> <font color="Olive" title="b3">x2</font></span>)</span>)</div></div>
