<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th14</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: HALLMAR1:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">J</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K2" title="HALLMAR1:func.2">Cut</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">i</font>,<font color="Olive" title="b4">x</font>)</span>)</span> &amp; <font color="Olive" title="b3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">J</font> holds <br/> <a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<span class="p1">(<span class="default"><a href="hallmar1.html#K2" title="HALLMAR1:func.2">Cut</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">i</font>,<font color="Olive" title="b4">x</font>)</span>)</span>,<font color="Olive" title="b5">J</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K1" title="HALLMAR1:func.1">union</a> (<font color="Olive" title="b2">A</font>,<span class="p2">(<span class="default"><font color="Olive" title="b5">J</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">i</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>)</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></div></div>
