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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: SURREALO:47</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> 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="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff  ex <font color="Olive" title="b2">y</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) )</div></div>
