<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: NECKLA_3:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="necklace.html#V1" title="NECKLACE:attr.1">symmetric</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">R1</font>, <font color="Olive" title="b4">R2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">R1</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b4">R2</font> &amp;  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="neckla_2.html#K1" title="NECKLA_2:func.1">union_of</a> (<font color="Olive" title="b3">R1</font>,<font color="Olive" title="b4">R2</font>) &amp; <font color="Olive" title="b1">G</font> is  <a href="neckla_3.html#V1" title="NECKLA_3:attr.1">path-connected</a>  holds <br/> ex <font color="Olive" title="b5">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b3">R1</font> st <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b5">b</font>,<font color="Olive" title="b2">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Olive" title="b1">G</font></div></div>
