<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:66_1_1"/>
<font color="Maroon">S</font> <a href="borsuk_1.html#K3">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">T</font></span>)</span> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D37">WAYBEL_0:def 37</a><br/>

<b>thus </b><a NAME="E1:66_1_1_1"/>
( <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">X</font> is <a href="waybel_0.html#V1">directed</a> or <font color="Maroon">S</font> <a href="borsuk_1.html#K3">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">T</font></span>)</span> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Maroon">X</font> )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:66_1_1"/>
<font color="Maroon">S</font> <a href="borsuk_1.html#K3">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">T</font></span>)</span> is <a href="waybel_0.html#V17">infs-preserving</a>
 <b>by </b><i/>;<br/>


</div>
