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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">S</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">S</font>
 ;<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="E3:1_1_1"/><i><font color="Green">E30</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">S</font>
 <b>by </b><i><a class="ref" href="funct_5.html#D1">FUNCT_5:def 1</a></i>;<br/><a NAME="E4:1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/><b>hence </b><a NAME="E5:1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="funct_5.html#D2">FUNCT_5:def 2</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">S</font>
 ;<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="E4:1_1"/><i><font color="Green">E31</font></i>: 
<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">S</font>
 <b>by </b><i><a class="ref" href="funct_5.html#D2">FUNCT_5:def 2</a></i>;<br/><a NAME="E5:1_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/><b>hence </b><a NAME="E6:1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="funct_5.html#D1">FUNCT_5:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:1"/>
 <a href="funct_5.html#K1">proj1</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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