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<span class="kw">let </span><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">X9</font>, <font color="Maroon" title="c10">Y1</font>, <font color="Maroon" title="c11">Y2</font>, <font color="Maroon" title="c12">Y3</font>, <font color="Maroon" title="c13">Y4</font>, <font color="Maroon" title="c14">Y5</font>, <font color="Maroon" title="c15">Y6</font>, <font color="Maroon" title="c16">Y7</font>, <font color="Maroon" title="c17">Y8</font>, <font color="Maroon" title="c18">Y9</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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>,<font color="Maroon" title="c9">X9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> <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; <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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>,<font color="Maroon" title="c9">X9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</a><span class="default"><font color="Maroon" title="c10">Y1</font>,<font color="Maroon" title="c11">Y2</font>,<font color="Maroon" title="c12">Y3</font>,<font color="Maroon" title="c13">Y4</font>,<font color="Maroon" title="c14">Y5</font>,<font color="Maroon" title="c15">Y6</font>,<font color="Maroon" title="c16">Y7</font>,<font color="Maroon" title="c17">Y8</font>,<font color="Maroon" title="c18">Y9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> implies ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">Y8</font> &amp; <font color="Maroon" title="c9">X9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">Y9</font> ) )</span><br/>



































<span class="kw">assume </span><a NAME="E1:152"/><span class="lab"><font color="Green" title="E101">A1</font></span>: 
<span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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>,<font color="Maroon" title="c9">X9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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>,<font color="Maroon" title="c9">X9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</a><span class="default"><font color="Maroon" title="c10">Y1</font>,<font color="Maroon" title="c11">Y2</font>,<font color="Maroon" title="c12">Y3</font>,<font color="Maroon" title="c13">Y4</font>,<font color="Maroon" title="c14">Y5</font>,<font color="Maroon" title="c15">Y6</font>,<font color="Maroon" title="c16">Y7</font>,<font color="Maroon" title="c17">Y8</font>,<font color="Maroon" title="c18">Y9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> or ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">Y8</font> &amp; <font color="Maroon" title="c9">X9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">Y9</font> ) )</span><br/>

<a NAME="E2:152"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A2</font></span>: 
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_2.html#T174" target="_self" title="MCART_2:th.174">Th176</a></span>;<br/>
<a NAME="E3:152"/><span class="lab"><font color="Green" title="E103">A3</font></span>: 
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:152"><span class="lab"><font color="Green" title="E101">A1</font></span></a>, <a class="ref" href="mcart_2.html#T174" target="_self" title="MCART_2:th.174">Th176</a></span>;<br/>
<a NAME="E4:152"/><span class="lab"><font color="Green" title="E104">A4</font></span>: 
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:152"><span class="lab"><font color="Green" title="E101">A1</font></span></a>, <a class="ref" href="mcart_2.html#T174" target="_self" title="MCART_2:th.174">Th176</a></span>;<br/>
<a NAME="E5:152"/><span class="lab"><font color="Green" title="E105">A5</font></span>: 
<font color="Maroon" title="c9">X9</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:152"><span class="lab"><font color="Green" title="E101">A1</font></span></a>, <a class="ref" href="mcart_2.html#T174" target="_self" title="MCART_2:th.174">Th176</a></span>;<br/>
<a NAME="E6:152"/>
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:152"><span class="lab"><font color="Green" title="E101">A1</font></span></a>, <a class="ref" href="mcart_2.html#T174" target="_self" title="MCART_2:th.174">Th176</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:152"/>
(  not <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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>,<font color="Maroon" title="c9">X9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</a><span class="default"><font color="Maroon" title="c10">Y1</font>,<font color="Maroon" title="c11">Y2</font>,<font color="Maroon" title="c12">Y3</font>,<font color="Maroon" title="c13">Y4</font>,<font color="Maroon" title="c14">Y5</font>,<font color="Maroon" title="c15">Y6</font>,<font color="Maroon" title="c16">Y7</font>,<font color="Maroon" title="c17">Y8</font>,<font color="Maroon" title="c18">Y9</font></span><a href="mcart_2.html#K37" title="MCART_2:func.37">:]</a></span> or ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">Y8</font> &amp; <font color="Maroon" title="c9">X9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">Y9</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:152"><span class="lab"><font color="Green" title="E102">A2</font></span></a>, <a class="txt" href="#E4:152"><span class="lab"><font color="Green" title="E104">A4</font></span></a>, <a class="txt" href="#E3:152"><span class="lab"><font color="Green" title="E103">A3</font></span></a>, <a class="txt" href="#E5:152"><span class="lab"><font color="Green" title="E105">A5</font></span></a>, <a class="ref" href="mcart_2.html#T175" target="_self" title="MCART_2:th.175">Th177</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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