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<b>thus </b><a NAME="E1:67_1_1"/>
<font color="Maroon" title="c1">S</font> <a href="borsuk_1.html#K3" title="BORSUK_1:func.3">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">T</font></span>)</span> is <a href="waybel_0.html#V21" title="WAYBEL_0:attr.21">filtered-infs-preserving</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D36" title="WAYBEL_0:def.36">WAYBEL_0:def 36</a><br/>

<b>thus </b><a NAME="E1:67_1_1_1"/>
( <font color="Maroon" title="c3">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c3">X</font> is <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a> or <font color="Maroon" title="c1">S</font> <a href="borsuk_1.html#K3" title="BORSUK_1:func.3">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="waybel_0.html#R3" title="WAYBEL_0:pred.3">preserves_inf_of</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="ref" href="waybel34.html#T44" target="_self" title="WAYBEL34:th.44">Th44</a></i>;<br/>


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

<b>thus </b><a NAME="E2:67_1_1"/>
<font color="Maroon" title="c1">S</font> <a href="borsuk_1.html#K3" title="BORSUK_1:func.3">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">T</font></span>)</span> is <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a>
 <b>by </b><i><a class="ref" href="waybel34.html#T45" target="_self" title="WAYBEL34:th.45">Th45</a></i>;<br/>


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