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

<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="pencil_1.html#V15">PLS-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> holds  <font color="Maroon">A</font> <a href="pencil_1.html#K2">.</a> <font color="Olive">i</font> is <a href="pencil_1.html#V10">strongly_connected</a>
 ;<br/>

<b>let </b><font color="Maroon">B</font> be    <a href="pencil_2.html#M1" target="_self">Segre-Coset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="pencil_2.html#NM2">Collineation</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span>;<br/>



<a NAME="E2:33"/>
<font color="Maroon">f</font> is <a href="funct_2.html#V3">bijective</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:33"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">f</font> is <a href="funct_2.html#V2">onto</a> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D4">FUNCT_2:def 4</a></i>;<br/>
<a NAME="E4:33"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> <a href="tops_2.html#NK3" target="_self">"</a>  as   <a href="pencil_2.html#NM2">Collineation</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E7:33"/><i><font color="Green">E36</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">W</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span><b> such that </b><br/><a NAME="E9:33"/><i><font color="Green">E43</font></i>: 
( not <font color="Maroon">W</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">W</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">W</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span>  )
 <b>by </b><i>, </i>;<br/>
<a NAME="E10:33"/><i><font color="Green">E48</font></i>: 
( not <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font> is <a href="pencil_1.html#V1">closed_under_lines</a> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E11:33"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:33_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</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="E1:33_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon">u</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:33_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:33_1_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </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">Y</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span><b> such that </b><br/><a NAME="E7:33_1_1"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">W</font>,<font color="Maroon">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  )
 <b>by </b><i/>;<br/>
<a NAME="E8:33_1_1"/><i><font color="Green">E52</font></i>: 
( not <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> )
 
<b>by </b><i><a class="ref" href="pencil_2.html#T1" target="_self">Th1</a>, , , </i>;<br/>
<a NAME="E9:33_1_1"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a> 
 
<b>by </b><i>, <a class="ref" href="pencil_2.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E10:33_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">Z</font> where <font color="Olive">Z</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Z</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Z</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Z</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Olive">Z</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="pencil_2.html#E1:33"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E11:33_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , <a class="ref" href="pencil_2.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E12:33_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span> 
 <b>by </b><i><a class="txt" href="pencil_2.html#E3:33"><i><font color="Green">E33</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">o</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="E2:33_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">u</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:33_1"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">u</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">Y</font> where <font color="Olive">Y</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Olive">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </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">Y</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span><b> such that </b><br/><a NAME="E6:33_1"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font>,<font color="Maroon">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  )
 <b>by </b><i/>;<br/>
<a NAME="E7:33_1"/>
( not <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font> is <a href="pencil_1.html#V1">closed_under_lines</a> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E8:33_1"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font></span>)</span>,<font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:33_1"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">W</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T152">FUNCT_1:152</a></i>;<br/>
<a NAME="E10:33_1"/>
<font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T146">FUNCT_1:146</a></i>;<br/>
<a NAME="E11:33_1"/><b>then </b>
<font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">W</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="txt" href="pencil_2.html#E1:33"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E12:33_1"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">W</font>,<font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a> 
 
<b>by </b><i>, , <a class="ref" href="pencil_2.html#T1" target="_self">Th1</a>, <a class="ref" href="tops_2.html#T68">TOPS_2:68</a></i>;<br/>
<a NAME="E13:33_1"/>
( not <font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> is <a href="pencil_1.html#V1">closed_under_lines</a> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E14:33_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">Z</font> where <font color="Olive">Z</font> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K6">Segre_Product</a> <font color="Maroon">A</font></span>)</span> : ( not <font color="Olive">Z</font> is <a href="realset1.html#V1">trivial</a> &amp; <font color="Olive">Z</font> is <a href="pencil_1.html#V2">strong</a> &amp; <font color="Olive">Z</font> is <a href="pencil_1.html#V1">closed_under_lines</a> &amp; <font color="Maroon">W</font>,<font color="Olive">Z</font> <a href="pencil_2.html#R1" target="_self">are_joinable</a>  ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="pencil_2.html#E3:33"><i><font color="Green">E33</font></i></a></i>;<br/>
<a NAME="E15:33_1"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">g</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E16:33_1"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 
<b>by </b><i>, <a class="txt" href="pencil_2.html#E4:33"><i><font color="Green">E34</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E17:33_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
 
<b>by </b><i>, , , , <a class="ref" href="funct_1.html#T57">FUNCT_1:57</a></i>;<br/>
<a NAME="E18:33_1"/><b>then </b>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<b>hence </b><a NAME="E19:33_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="txt" href="pencil_2.html#E5:33"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E12:33"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">B</font> is    <a href="pencil_2.html#M1" target="_self">Segre-Coset</a> of <font color="Maroon">A</font>
 <b>by </b><i>, , </i>;<br/>


</div>
