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

<b>set </b><font color="Maroon">FUF</font> =  <a href="waybel22.html#K1" target="_self">FixedUltraFilters</a> <font color="Maroon">X</font>;<br/>
<b>set </b><font color="Maroon">IP</font> =  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span>;<br/>
<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="orders_2.html#NM1">Poset</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel22.html#D1" target="_self">WAYBEL22:def 1</a><br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="waybel22.html#K1" target="_self">FixedUltraFilters</a> <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/>



<b>reconsider </b><font color="Maroon">F</font> = <font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a>  as    <a href="waybel16.html#M1">CLHomomorphism</a> of  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span>,<font color="Maroon">L</font> <b>by </b><i><a class="ref" href="waybel16.html#D1">WAYBEL16:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E2:25"/>
<font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="waybel22.html#K1" target="_self">FixedUltraFilters</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">h'</font> be    <a href="waybel16.html#M1">CLHomomorphism</a> of  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span>,<font color="Maroon">L</font>;<br/>

<b>assume </b><a NAME="E3:25"/>
<font color="Maroon">h'</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="waybel22.html#K1" target="_self">FixedUltraFilters</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 ;<br/>

<b>hence </b><a NAME="E4:25"/>
<font color="Maroon">h'</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/>


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