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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: SURREALN:31</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  <a href="surreal0.html#K12" title="SURREAL0:func.12">born</a> <font color="Olive" title="b1">x</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <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="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> 1 holds <br/> ex <font color="Olive" title="b2">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Olive" title="b1">x</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a> <a href="surrealn.html#K1" title="SURREALN:func.1">uInt</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font></div></div>
