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<div><span class="kw">theorem </span><a NAME="T49"><span class="comment"><font color="firebrick">:: SURREALO:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st (  for <font color="Olive" title="b2">z</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b2">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surrealo.html#K3" title="SURREALO:func.3">born_eq_set</a> <font color="Olive" title="b1">x</font> &amp; <span class="p1">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b2">z</font></span>)</span> is  <a href="surrealo.html#V3" title="SURREALO:attr.3">uniq-surreal-membered</a>  &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">z</font> holds <br/><span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p2">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b1">x</font></span>)</span></span>)</span> <a href="ordinal7.html#K5" title="ORDINAL7:func.5">(+)</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p2">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b1">x</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p2">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b2">z</font></span>)</span></span>)</span> <a href="ordinal7.html#K5" title="ORDINAL7:func.5">(+)</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p2">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b2">z</font></span>)</span></span>)</span> ) &amp; <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surrealo.html#K3" title="SURREALO:func.3">born_eq_set</a> <font color="Olive" title="b1">x</font> &amp; <span class="p1">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b1">x</font></span>)</span> is  <a href="surrealo.html#V3" title="SURREALO:attr.3">uniq-surreal-membered</a>  holds <br/><font color="Olive" title="b1">x</font> is   <a href="surrealo.html#NM1" title="SURREALO:NM.1">uSurreal</a></div></div>
