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<b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X3</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X4</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X5</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X6</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y3</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y4</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y5</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y6</font> be    <a href="hidden.html#M1">set</a> ;<br/>























<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">X1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X4</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X5</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X6</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">Y1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Y2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Y3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Y4</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Y5</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">Y6</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="mcart_3.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font>,<font color="Maroon">X3</font>,<font color="Maroon">X4</font>,<font color="Maroon">X5</font>,<font color="Maroon">X6</font></span><a href="mcart_3.html#K2" target="_self">:]</a></span>;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="mcart_3.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">Y1</font>,<font color="Maroon">Y2</font>,<font color="Maroon">Y3</font>,<font color="Maroon">Y4</font>,<font color="Maroon">Y5</font>,<font color="Maroon">Y6</font></span><a href="mcart_3.html#K2" target="_self">:]</a></span>;<br/>



<b>assume </b><a NAME="E3:35"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="mcart_3.html#K3" target="_self">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="mcart_3.html#K3" target="_self">`1</a> 
<b>by </b><i>, , </i>
;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="mcart_3.html#K4" target="_self">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="mcart_3.html#K4" target="_self">`2</a> 
<b>by </b><i>, , </i>
;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="mcart_3.html#K5" target="_self">`3</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="mcart_3.html#K5" target="_self">`3</a> 
<b>by </b><i>, , </i>
;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="mcart_3.html#K6" target="_self">`4</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="mcart_3.html#K6" target="_self">`4</a> 
<b>by </b><i>, , </i>
;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="mcart_3.html#K7" target="_self">`5</a>  = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="mcart_3.html#K7" target="_self">`5</a> 
<b>by </b><i>, , </i>
;<br/>

<b>thus </b><font color="Maroon">x</font> <a href="mcart_3.html#K8" target="_self">`6</a>  = 
<font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="mcart_3.html#K8" target="_self">`6</a> 
<b>by </b><i>, , </i>
;<br/>


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