<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: JORDAN3:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">q</font> &amp;  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font>) &amp;  <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>)</span>)</span>,<font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2" title="JORDAN3:func.2">L_Cut</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">p</font>)</span>)</span></div></div>
