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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">X1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">Y1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/>







<b>assume </b><a NAME="E1:7"/><i><font color="Green">E24</font></i>: 
<span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="mcart_1.html#K12">:]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="funct_3.html#K1">.:</a> <span class="p2">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="mcart_1.html#K12">:]</a></span> = 
<span class="p1">(<span class="default"><a href="funct_3.html#K9">pr1</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="mcart_1.html#K12">:]</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">X1</font>
<b>by </b><i>, </i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="funct_3.html#K1">.:</a> <span class="p2">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="mcart_1.html#K12">:]</a></span> = 
<span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">Y1</font></span><a href="mcart_1.html#K12">:]</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">Y1</font>
<b>by </b><i>, </i>
;<br/>


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