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<a NAME="E1:23_1_1"/>
 <a href="card_3.html#K5">pi</a> <font color="Maroon">X</font>,<font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">z</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="E1:23_1_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <font color="Maroon">X</font>,<font color="Maroon">i</font>
 ;<br/>

<b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:23_1_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">M</font> <b>by </b><i>, <a class="ref" href="msualg_5.html#D5">MSUALG_5:def 5</a></i>;<br/>
<a NAME="E5:23_1_1_1"/>
<font color="Maroon">f</font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">i</font> is   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i><a class="ref" href="msualg_4.html#D3">MSUALG_4:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1_1"/>
<font color="Maroon">z</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="msualg_5.html#K2">EqRelLatt</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="msualg_7.html#T1">MSUALG_7:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:23_1_1"/>
 <a href="msualg_8.html#NK3" target="_self">EqRelSet</a> , is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K2">EqRelLatt</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 ;<br/>


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