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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">FUF</font> =  <a href="waybel22.html#K1" title="WAYBEL22:func.1">FixedUltraFilters</a> <font color="Maroon" title="c1">X</font>;<br/>
<b>set </b><font color="Maroon" title="c3">IP</font> =  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K8" title="WAYBEL_0:func.8">Filt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c4">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel22.html#D1" target="_self" title="WAYBEL22:def.1">WAYBEL22:def 1</a><br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="waybel22.html#K1" title="WAYBEL22:func.1">FixedUltraFilters</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">L</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c6">F</font> = <font color="Maroon" title="c5">f</font> <a href="waybel22.html#K2" title="WAYBEL22:func.2">-extension_to_hom</a>  as    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K8" title="WAYBEL_0:func.8">Filt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">L</font> <b>by </b><i><a class="ref" href="waybel16.html#D1" title="WAYBEL16:def.1">WAYBEL16:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">F</font>
;<br/>

<b>thus </b><a NAME="E2:25"/>
<font color="Maroon" title="c6">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="waybel22.html#K1" title="WAYBEL22:func.1">FixedUltraFilters</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font>
 <b>by </b><i><a class="ref" href="waybel22.html#T14" target="_self" title="WAYBEL22:th.14">Th14</a></i>;<br/>

<b>let </b><font color="Maroon" title="c7">h'</font> be    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K8" title="WAYBEL_0:func.8">Filt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">L</font>;<br/>

<b>assume </b><a NAME="E3:25"/>
<font color="Maroon" title="c7">h'</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="waybel22.html#K1" title="WAYBEL22:func.1">FixedUltraFilters</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font>
 ;<br/>

<b>hence </b><a NAME="E4:25"/>
<font color="Maroon" title="c7">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">F</font>
 <b>by </b><i><a class="ref" href="waybel22.html#T15" target="_self" title="WAYBEL22:th.15">Th15</a></i>;<br/>


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