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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">x9</font>, <font color="Maroon" title="c10">X1</font>, <font color="Maroon" title="c11">X2</font>, <font color="Maroon" title="c12">X3</font>, <font color="Maroon" title="c13">X4</font>, <font color="Maroon" title="c14">X5</font>, <font color="Maroon" title="c15">X6</font>, <font color="Maroon" title="c16">X7</font>, <font color="Maroon" title="c17">X8</font>, <font color="Maroon" title="c18">X9</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</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_3.html#K28" title="MCART_3:func.28">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c10">X1</font>,<font color="Maroon" title="c11">X2</font>,<font color="Maroon" title="c12">X3</font>,<font color="Maroon" title="c13">X4</font>,<font color="Maroon" title="c14">X5</font>,<font color="Maroon" title="c15">X6</font>,<font color="Maroon" title="c16">X7</font>,<font color="Maroon" title="c17">X8</font>,<font color="Maroon" title="c18">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span> iff ( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X1</font> &amp; <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">X2</font> &amp; <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">X3</font> &amp; <font color="Maroon" title="c4">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">X4</font> &amp; <font color="Maroon" title="c5">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">X5</font> &amp; <font color="Maroon" title="c6">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">X6</font> &amp; <font color="Maroon" title="c7">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">X7</font> &amp; <font color="Maroon" title="c8">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">X8</font> &amp; <font color="Maroon" title="c9">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">X9</font> ) )</span><br/>



































<a NAME="E1:142"/><i><font color="Green" title="E92">A1</font></i>: 
<span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c10">X1</font>,<font color="Maroon" title="c11">X2</font>,<font color="Maroon" title="c12">X3</font>,<font color="Maroon" title="c13">X4</font>,<font color="Maroon" title="c14">X5</font>,<font color="Maroon" title="c15">X6</font>,<font color="Maroon" title="c16">X7</font>,<font color="Maroon" title="c17">X8</font>,<font color="Maroon" title="c18">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K19" title="MCART_3:func.19">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">X1</font>,<font color="Maroon" title="c11">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c12">X3</font>,<font color="Maroon" title="c13">X4</font>,<font color="Maroon" title="c14">X5</font>,<font color="Maroon" title="c15">X6</font>,<font color="Maroon" title="c16">X7</font>,<font color="Maroon" title="c17">X8</font>,<font color="Maroon" title="c18">X9</font></span><a href="mcart_3.html#K19" title="MCART_3:func.19">:]</a></span>
 
<b>by </b><i><a class="ref" href="mcart_3.html#T51" target="_self" title="MCART_3:th.51">MC351</a></i>;<br/>
<a NAME="E2:142"/><i><font color="Green" title="E93">A2</font></i>: 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</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_3.html#K28" title="MCART_3:func.28">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K18" title="MCART_3:func.18">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<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_3.html#K18" title="MCART_3:func.18">]</a></span>
 
<b>by </b><i><a class="ref" href="mcart_3.html#T44" target="_self" title="MCART_3:th.44">MC344</a></i>;<br/>
<a NAME="E3:142"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">X1</font>,<font color="Maroon" title="c11">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> iff ( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X1</font> &amp; <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">X2</font> ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E4:142"/>
( <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</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_3.html#K28" title="MCART_3:func.28">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c10">X1</font>,<font color="Maroon" title="c11">X2</font>,<font color="Maroon" title="c12">X3</font>,<font color="Maroon" title="c13">X4</font>,<font color="Maroon" title="c14">X5</font>,<font color="Maroon" title="c15">X6</font>,<font color="Maroon" title="c16">X7</font>,<font color="Maroon" title="c17">X8</font>,<font color="Maroon" title="c18">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span> iff ( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X1</font> &amp; <font color="Maroon" title="c2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">X2</font> &amp; <font color="Maroon" title="c3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">X3</font> &amp; <font color="Maroon" title="c4">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">X4</font> &amp; <font color="Maroon" title="c5">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">X5</font> &amp; <font color="Maroon" title="c6">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">X6</font> &amp; <font color="Maroon" title="c7">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">X7</font> &amp; <font color="Maroon" title="c8">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">X8</font> &amp; <font color="Maroon" title="c9">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">X9</font> ) )
 <b>by </b><i><a class="txt" href="mcart_3.html#E1:142"><i><font color="Green" title="E92">A1</font></i></a>, <a class="txt" href="mcart_3.html#E2:142"><i><font color="Green" title="E93">A2</font></i></a>, <a class="ref" href="mcart_3.html#T115" target="_self" title="MCART_3:th.115">Th38</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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