<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: SURREALI:12</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><br/>  for <font color="Olive" title="b2">Inv</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds   <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p1">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">Inv</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<span class="p3">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p4">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">Inv</font>)</span>)</span></span>)</span>,<font color="Olive" title="b1">x</font>,<span class="p3">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Olive" title="b2">Inv</font>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<span class="p2">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p3">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">Inv</font>)</span>)</span></span>)</span>,<font color="Olive" title="b1">x</font>,<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>,<font color="Olive" title="b2">Inv</font>)</span>)</span></div></div>
