<?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>set </b><font color="Maroon">F</font> = <font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> ;<br/>
<b>let </b><font color="Maroon">Fs</font> be   <a href="struct_0.html#NM2">Subset</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>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D37">WAYBEL_0:def 37</a><br/>

<b>assume </b><a NAME="E1:21_1_1"/><i><font color="Green">E31</font></i>: 
( not <font color="Maroon">Fs</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">Fs</font> is <a href="waybel_0.html#V1">directed</a> )
 ;<br/>

<b>assume </b><a NAME="E2:21_1_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">Fs</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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D31">WAYBEL_0:def 31</a><br/>

<b>thus </b><a NAME="E3:21_1_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Fs</font>,<font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>

<a NAME="E4:21_1_1"/><i><font color="Green">E35</font></i>: 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">Fs</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">Fs</font>
 
<b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">Fs'</font> = <font color="Maroon">Fs</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</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>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">sFs</font> =  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">Fs</font> as   <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> ;<br/>
<a NAME="E7:21_1_1"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">sFs</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="Maroon">sFs</font> </span>}</span> ,<font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">FFs</font> = <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">sFs</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon">FFsU</font> = <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">Zs</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">Z</font></span>)</span> where <font color="Olive">Z</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> : <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span>  </span>}</span> ;<br/>
<a NAME="E8:21_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">r</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:21_1_1_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">YY</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font><b> such that </b><br/><a NAME="E3:21_1_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R1">=</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">YY</font> </span>}</span> 
 ;<br/>
<a NAME="E4:21_1_1_1"/>
<font color="Maroon">r</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:21_1_1_1_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font>
 ;<br/>

<b>then consider </b><font color="Maroon">Y</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:21_1_1_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<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="Maroon">Y</font> ) </span>}</span> ,<font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E4:21_1_1_1_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">YY</font>
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E5:21_1_1_1_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:21_1_1_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E9:21_1_1"/><b>then </b><i><font color="Green">E60</font></i>: 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p5">{<span class="default"> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> </span>)</span>,<font color="Maroon">L</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#NK3" target="_self">sup</a> <font color="Olive">Z</font></span>)</span> where <font color="Olive">Z</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> : <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span>  </span>}</span> ,<font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:21_1_1_2_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</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">sFs</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">Y</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:21_1_1_2_1"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<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="Maroon">Y</font> ) </span>}</span> ,<font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E4:21_1_1_2_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">sFs</font>
 ;<br/><b>consider </b><font color="Maroon">YY</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:21_1_1_2_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">YY</font>
 <b>and </b><br/><a NAME="E7:21_1_1_2_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">YY</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Fs</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><a NAME="E8:21_1_1_2_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</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">Y1</font> ) </span>}</span> ,<font color="Maroon">L</font></span>)</span> where <font color="Olive">Y1</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : <font color="Olive">Y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">YY</font> </span>}</span> 
 <b>by </b><i>, </i>;<br/><a NAME="E9:21_1_1_2_1"/>
<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">Y1</font> ) </span>}</span> ,<font color="Maroon">L</font></span>)</span> where <font color="Olive">Y1</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : <font color="Olive">Y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">YY</font> </span>}</span>  <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E10:21_1_1_2_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:21_1_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">r</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:21_1_1_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E5:21_1_1_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon">YY</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font><b> such that </b><br/><a NAME="E7:21_1_1_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R1">=</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">YY</font> </span>}</span> 
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">Y</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E9:21_1_1_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<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="Maroon">Y</font> ) </span>}</span> ,<font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E10:21_1_1_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">YY</font>
 <b>by </b><i>, </i>;<br/><a NAME="E11:21_1_1_2"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">sFs</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><b>hence </b><a NAME="E12:21_1_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</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">sFs</font> </span>}</span> 
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E11:21_1_1"/><b>then </b><i><font color="Green">E73</font></i>: 
<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">sFs</font> </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">r</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:21_1_1_3_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Fs</font>
 ;<br/><b>then consider </b><font color="Maroon">YY</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:21_1_1_3_1"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">YY</font> <a href="hidden.html#R2">in</a> 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>
 <b>and </b><br/><a NAME="E4:21_1_1_3_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">YY</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Fs</font>
 <b>and </b><br/><a NAME="E5:21_1_1_3_1"/><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">YY</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T115">FUNCT_2:115</a></i>;<br/><b>reconsider </b><font color="Maroon">YY</font> = <font color="Maroon">YY</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Fs</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">YY'</font> = <font color="Maroon">YY</font> as   <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>by </b><i/>;<br/><a NAME="E8:21_1_1_3_1"/><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">YY'</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="Maroon">YY'</font> </span>}</span> ,<font color="Maroon">L</font>
 <b>by </b><i/>;<br/><b>set </b><font color="Maroon">Zi</font> = <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">YY'</font> </span>}</span> ;<br/><a NAME="E9:21_1_1_3_1"/>
<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">YY'</font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_3_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:21_1_1_3_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</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">YY'</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">Y</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:21_1_1_3_1_1"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<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="Maroon">Y</font> ) </span>}</span> ,<font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E4:21_1_1_3_1_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">YY'</font>
 ;<br/>
<b>thus </b><a NAME="E5:21_1_1_3_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon">Zi</font> = <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">YY'</font> </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/><a NAME="E11:21_1_1_3_1"/>
<font color="Maroon">Zi</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 ;<br/><b>hence </b><a NAME="E12:21_1_1_3_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">Z</font></span>)</span> where <font color="Olive">Z</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> : <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span>  </span>}</span> 
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:21_1_1_3"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">Z</font></span>)</span> where <font color="Olive">Z</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> : <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span>  </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">Z</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:21_1_1_3"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">Z</font>
 <b>and </b><br/><a NAME="E5:21_1_1_3"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="yellow_0.html#K2">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p0">(<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">YY</font> </span>}</span>  where <font color="Olive">YY</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> : verum </span>}</span> 
 ;<br/><b>consider </b><font color="Maroon">YY</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Fs</font><b> such that </b><br/><a NAME="E7:21_1_1_3"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</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">YY</font> </span>}</span> 
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">YY</font> = <font color="Maroon">YY</font> as    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Fs'</font> ;<br/><b>reconsider </b><font color="Maroon">YY'</font> = <font color="Maroon">YY</font> as   <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> ;<br/><a NAME="E10:21_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">YY'</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="Maroon">YY'</font> </span>}</span> ,<font color="Maroon">L</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E11:21_1_1_3"/>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Fs</font>
 <b>by </b><i>, , <a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:21_1_1"/>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Fs</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="waybel22.html#K2" target="_self">-extension_to_hom</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">Fs</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
