<?xml version="1.0"?>
<div class="add">

<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>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> =  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">x</font></span>)</span></span>)</span> where <font color="Olive">x</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span> :  ex <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">z</font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> ) </span>}</span> ,<font color="Maroon">L</font></span>)</span> where <font color="Olive">Y</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a<sub>1</sub></font> </span>}</span> ,<font color="Maroon">L</font>;<br/>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:18_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">Fi</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span> holds  <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">Fi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">Fi</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<b>reconsider </b><font color="Maroon">F</font> = <font color="Maroon">F</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">L</font> ;<br/>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E4:18_1_1"/>
for <font color="Olive">Fi</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K8">Filt</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span> holds  <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">Fi</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p5">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Olive">x</font></span>)</span></span>)</span> where <font color="Olive">x</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span> :  ex <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">z</font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> ) </span>}</span> ,<font color="Maroon">L</font></span>)</span> where <font color="Olive">Y</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <font color="Olive">Fi</font> </span>}</span> ,<font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


</div>
