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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="cohsp_1.html#R1" title="COHSP_1:pred.1">includes_lattice_of</a> <font color="Maroon" title="c1">X</font> implies ( <font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V1" title="COHSP_1:attr.1">c=directed</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V2" title="COHSP_1:attr.2">c=filtered</a> ) )</span><br/>

<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E16">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/>( <font color="Olive" title="b1">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cohsp_1.html#D8" target="_self" title="COHSP_1:def.8">COHSP_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V1" title="COHSP_1:attr.1">c=directed</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V2" title="COHSP_1:attr.2">c=filtered</a> )</span><br/>

<a NAME="E2:38"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/> ex <font color="Olive" title="b3">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E1:38"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:38"/>
<font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V1" title="COHSP_1:attr.1">c=directed</a>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T6" target="_self" title="COHSP_1:th.6">Th6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V2" title="COHSP_1:attr.2">c=filtered</a></span><br/>

<a NAME="E4:38"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/> ex <font color="Olive" title="b3">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">a</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E1:38"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V2" title="COHSP_1:attr.2">c=filtered</a>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T8" target="_self" title="COHSP_1:th.8">Th8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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