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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:34_1_1_1"/>
<font color="Maroon">F</font> is <a href="functor0.html#V6" target="_self">reflexive</a>
 ;<br/><a NAME="E2:34_1_1_1"/><b>then </b><i><font color="Green">E20</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>
 <b>by </b><i/>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><a NAME="E3:34_1_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/><a NAME="E4:34_1_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/><b>then consider </b><font color="Maroon">p</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">p'</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:34_1_1_1"/><i><font color="Green">E26</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">p'</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a></i>;<br/><a NAME="E7:34_1_1_1"/>
<font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E8:34_1_1_1"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, , , <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:34_1_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">o</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font> holds  the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Olive">o</font>,<font color="Olive">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Olive">o</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Olive">o</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<b>let </b><font color="Maroon">x</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>,<a class="ref" href="functor0.html#D9" target="_self">FUNCTOR0:def 9</a><br/>

<b>assume </b><a NAME="E3:34_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:34_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E6:34_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E7:34_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T115">FUNCT_2:115</a></i>;<br/>
<b>consider </b><font color="Maroon">o</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">o'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E9:34_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o'</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, <a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/>
<b>reconsider </b><font color="Maroon">o</font> = <font color="Maroon">o</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font> ;<br/>
<a NAME="E11:34_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o'</font>
 
<b>by </b><i>, <a class="txt" href="functor0.html#E5:34_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>
<a NAME="E12:34_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="functor0.html#E2:34_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="functor0.html#E5:34_1_1"><i><font color="Green">E31</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E13:34_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


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