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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">EqR</font> be   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:28"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>thus </b><a NAME="E2:28"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font> implies  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E39</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:28_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font>
 ;<br/><a NAME="E2:28_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 <b>by </b><i/>;<br/><a NAME="E3:28_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:28_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E3:28_1"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:28_1_2"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font>
 ;<br/><a NAME="E2:28_1_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 <b>by </b><i/>;<br/><a NAME="E3:28_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:28_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:28_1_2"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E5:28_1"/><b>then </b>
 <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:28_1"/>
 <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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

<b>assume </b><a NAME="E3:28"/>
 <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font>
 ;<br/>

<a NAME="E4:28"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7" target="_self">Class</a> <font color="Maroon">EqR</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:28"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">EqR</font>
 <b>by </b><i/>;<br/>


</div>
