<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th38</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: SURREALO:38</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b3">x</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="surrealo.html#K5" title="SURREALO:func.5">unique_No_op</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">B</font> holds <br/>(  <a href="surrealo.html#K2" title="SURREALO:func.2">born_eq</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K12" title="SURREAL0:func.12">born</a> <font color="Olive" title="b3">x</font> &amp;  <a href="surreal0.html#K12" title="SURREAL0:func.12">born</a> <font color="Olive" title="b3">x</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="surrealo.html#K5" title="SURREALO:func.5">unique_No_op</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="surreal0.html#K12" title="SURREAL0:func.12">born</a> <font color="Olive" title="b3">x</font></span>)</span> &amp;  not <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="surrealo.html#K5" title="SURREALO:func.5">unique_No_op</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p3">(<span class="default"><a href="surreal0.html#K12" title="SURREAL0:func.12">born</a> <font color="Olive" title="b3">x</font></span>)</span></span>)</span></span>)</span> )</div></div>
