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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">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="mcart_2.html#K36" title="MCART_2:func.36">[</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#K36" title="MCART_2:func.36">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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_2.html#K37" title="MCART_2:func.37">:]</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="E1:172"/><span class="lab"><font color="Green" title="E113">A1</font></span>: 
( <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> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E2:172"/>
( <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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_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#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span> &amp; <span class="p1"><a href="mcart_2.html#K36" title="MCART_2:func.36">[</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#K36" title="MCART_2:func.36">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K26" title="MCART_2:func.26">[</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_2.html#K26" title="MCART_2:func.26">]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_2.html#T6" target="_self" title="MCART_2:th.6">Th6</a>, <a class="ref" href="mcart_2.html#T12" target="_self" title="MCART_2:th.12">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:172"/>
( <span class="p1"><a href="mcart_2.html#K36" title="MCART_2:func.36">[</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#K36" title="MCART_2:func.36">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K37" title="MCART_2:func.37">[:</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_2.html#K37" title="MCART_2:func.37">:]</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:172"><span class="lab"><font color="Green" title="E113">A1</font></span></a>, <a class="ref" href="mcart_2.html#T153" target="_self" title="MCART_2:th.153">Th153</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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