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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">X3</font>, <font color="Maroon" title="c4">X4</font>, <font color="Maroon" title="c5">X5</font>, <font color="Maroon" title="c6">X6</font>, <font color="Maroon" title="c7">X7</font>, <font color="Maroon" title="c8">X8</font>, <font color="Maroon" title="c9">Y1</font>, <font color="Maroon" title="c10">Y2</font>, <font color="Maroon" title="c11">Y3</font>, <font color="Maroon" title="c12">Y4</font>, <font color="Maroon" title="c13">Y5</font>, <font color="Maroon" title="c14">Y6</font>, <font color="Maroon" title="c15">Y7</font>, <font color="Maroon" title="c16">Y8</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>































<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green" title="E23">A2</font></i>: 
( <font color="Maroon" title="c9">Y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">Y2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c11">Y3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c12">Y4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c13">Y5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c14">Y6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c15">Y7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c16">Y8</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon" title="c17">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_5.html#K2" title="MCART_5:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font>,<font color="Maroon" title="c4">X4</font>,<font color="Maroon" title="c5">X5</font>,<font color="Maroon" title="c6">X6</font>,<font color="Maroon" title="c7">X7</font>,<font color="Maroon" title="c8">X8</font></span><a href="mcart_5.html#K2" title="MCART_5:func.2">:]</a></span>;<br/><b>let </b><font color="Maroon" title="c18">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_5.html#K2" title="MCART_5:func.2">[:</a><span class="default"><font color="Maroon" title="c9">Y1</font>,<font color="Maroon" title="c10">Y2</font>,<font color="Maroon" title="c11">Y3</font>,<font color="Maroon" title="c12">Y4</font>,<font color="Maroon" title="c13">Y5</font>,<font color="Maroon" title="c14">Y6</font>,<font color="Maroon" title="c15">Y7</font>,<font color="Maroon" title="c16">Y8</font></span><a href="mcart_5.html#K2" title="MCART_5:func.2">:]</a></span>;<br/>



<b>assume </b><a NAME="E3:41"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font>
 ;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K3" title="MCART_5:func.3">`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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K3" title="MCART_5:func.3">`1</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K4" title="MCART_5:func.4">`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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K4" title="MCART_5:func.4">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K5" title="MCART_5:func.5">`3</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"><span class="p5">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K5" title="MCART_5:func.5">`3</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K6" title="MCART_5:func.6">`4</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" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K6" title="MCART_5:func.6">`4</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K7" title="MCART_5:func.7">`5</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K7" title="MCART_5:func.7">`5</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K8" title="MCART_5:func.8">`6</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K8" title="MCART_5:func.8">`6</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K9" title="MCART_5:func.9">`7</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K9" title="MCART_5:func.9">`7</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c17">x</font> <a href="mcart_5.html#K10" title="MCART_5:func.10">`8</a>  = 
<font color="Maroon" title="c17">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E1:41"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c18">y</font> <a href="mcart_5.html#K10" title="MCART_5:func.10">`8</a> 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:41"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="mcart_5.html#E3:41"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="mcart_5.html#T26" target="_self" title="MCART_5:th.26">Th26</a></i>
;<br/>


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