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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:38"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> holds <br/>( <font color="Olive">a</font> <a href="xboole_0.html#K3">/\</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cohsp_1.html#D8" target="_self">COHSP_1:def 8</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:38_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/><a NAME="E2:38_1"/><b>then </b>
<font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1"><i><font color="Green">Lemma16</font></i></a></i>;<br/><b>hence </b><a NAME="E3:38_1"/>
 ex <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> &amp; <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:38"/>
<font color="Maroon">X</font> is <a href="cohsp_1.html#V1" target="_self">c=directed</a>
 <b>by </b><i/>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:38_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/><a NAME="E2:38_2"/><b>then </b>
<font color="Maroon">a</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1"><i><font color="Green">Lemma16</font></i></a></i>;<br/><b>hence </b><a NAME="E3:38_2"/>
 ex <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">c</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font> &amp; <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon">X</font> is <a href="cohsp_1.html#V2" target="_self">c=filtered</a>
 <b>by </b><i/>;<br/>


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