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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">Z</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"> ( ( for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font> iff  ex <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">x3</font>, <font color="Olive" title="b5">x4</font>, <font color="Olive" title="b6">x5</font>, <font color="Olive" title="b7">x6</font>, <font color="Olive" title="b8">x7</font>, <font color="Olive" title="b9">x8</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> &amp; <font color="Olive" title="b3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Olive" title="b4">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X3</font> &amp; <font color="Olive" title="b5">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X4</font> &amp; <font color="Olive" title="b6">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X5</font> &amp; <font color="Olive" title="b7">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X6</font> &amp; <font color="Olive" title="b8">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X7</font> &amp; <font color="Olive" title="b9">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font> &amp; <font color="Olive" title="b1">y</font> <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"><font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font>,<font color="Olive" title="b4">x3</font>,<font color="Olive" title="b5">x4</font>,<font color="Olive" title="b6">x5</font>,<font color="Olive" title="b7">x6</font>,<font color="Olive" title="b8">x7</font>,<font color="Olive" title="b9">x8</font></span><a href="mcart_3.html#K18" title="MCART_3:func.18">]</a></span> ) ) ) implies <font color="Maroon" title="c9">Z</font> <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"><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_3.html#K19" title="MCART_3:func.19">:]</a></span> )</span><br/>

















<b>assume </b><a NAME="E1:107"/><i><font color="Green" title="E73">A1</font></i>: 
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font> iff  ex <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">x3</font>, <font color="Olive" title="b5">x4</font>, <font color="Olive" title="b6">x5</font>, <font color="Olive" title="b7">x6</font>, <font color="Olive" title="b8">x7</font>, <font color="Olive" title="b9">x8</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> &amp; <font color="Olive" title="b3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Olive" title="b4">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X3</font> &amp; <font color="Olive" title="b5">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X4</font> &amp; <font color="Olive" title="b6">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X5</font> &amp; <font color="Olive" title="b7">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X6</font> &amp; <font color="Olive" title="b8">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X7</font> &amp; <font color="Olive" title="b9">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font> &amp; <font color="Olive" title="b1">y</font> <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"><font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font>,<font color="Olive" title="b4">x3</font>,<font color="Olive" title="b5">x4</font>,<font color="Olive" title="b6">x5</font>,<font color="Olive" title="b7">x6</font>,<font color="Olive" title="b8">x7</font>,<font color="Olive" title="b9">x8</font></span><a href="mcart_3.html#K18" title="MCART_3:func.18">]</a></span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">Z</font> <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"><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_3.html#K19" title="MCART_3:func.19">:]</a></span></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">y</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"> ( ( <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font> implies <font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ) &amp; ( <font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font> ) )</span><br/><b>thus </b><a NAME="E1:107_1"/>
( <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font> implies <font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:107_1_1"/>
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c11">x1</font>, <font color="Maroon" title="c12">x2</font>, <font color="Maroon" title="c13">x3</font>, <font color="Maroon" title="c14">x4</font>, <font color="Maroon" title="c15">x5</font>, <font color="Maroon" title="c16">x6</font>, <font color="Maroon" title="c17">x7</font>, <font color="Maroon" title="c18">x8</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:107_1_1"/><i><font color="Green" title="E74">A2</font></i>: 
( <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> &amp; <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c13">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X3</font> &amp; <font color="Maroon" title="c14">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X4</font> &amp; <font color="Maroon" title="c15">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X5</font> &amp; <font color="Maroon" title="c16">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X6</font> &amp; <font color="Maroon" title="c17">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X7</font> &amp; <font color="Maroon" title="c18">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font> &amp; <font color="Maroon" title="c10">y</font> <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"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font>,<font color="Maroon" title="c13">x3</font>,<font color="Maroon" title="c14">x4</font>,<font color="Maroon" title="c15">x5</font>,<font color="Maroon" title="c16">x6</font>,<font color="Maroon" title="c17">x7</font>,<font color="Maroon" title="c18">x8</font></span><a href="mcart_3.html#K18" title="MCART_3:func.18">]</a></span> )
 <b>by </b><i><a class="txt" href="#E1:107"><i><font color="Green" title="E73">A1</font></i></a></i>;<br/>
<a NAME="E4:107_1_1"/>
( <span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font>,<font color="Maroon" title="c13">x3</font>,<font color="Maroon" title="c14">x4</font>,<font color="Maroon" title="c15">x5</font>,<font color="Maroon" title="c16">x6</font>,<font color="Maroon" title="c17">x7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span> &amp; <font color="Maroon" title="c18">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font> )
 
<b>by </b><i><a class="txt" href="#E3:107_1_1"><i><font color="Green" title="E74">A2</font></i></a>, <a class="ref" href="mcart_3.html#T72" target="_self" title="MCART_3:th.72">MC372</a></i>;<br/>
<b>hence </b><a NAME="E5:107_1_1"/>
<font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="#E3:107_1_1"><i><font color="Green" title="E74">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>assume </b><a NAME="E2:107_1"/>
<font color="Maroon" title="c10">y</font> <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"><span class="p2"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>,<font color="Maroon" title="c8">X8</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font></span><br/><b>then consider </b><font color="Maroon" title="c11">x1234567</font>, <font color="Maroon" title="c12">x8</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:107_1"/><i><font color="Green" title="E74">A3</font></i>: 
<font color="Maroon" title="c11">x1234567</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>
 <b>and </b><br/><a NAME="E5:107_1"/><i><font color="Green" title="E75">A4</font></i>: 
<font color="Maroon" title="c12">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font>
 <b>and </b><br/><a NAME="E6:107_1"/><i><font color="Green" title="E76">A5</font></i>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">x1234567</font>,<font color="Maroon" title="c12">x8</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c13">x1</font>, <font color="Maroon" title="c14">x2</font>, <font color="Maroon" title="c15">x3</font>, <font color="Maroon" title="c16">x4</font>, <font color="Maroon" title="c17">x5</font>, <font color="Maroon" title="c18">x6</font>, <font color="Maroon" title="c19">x7</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:107_1"/><i><font color="Green" title="E77">A6</font></i>: 
( <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X1</font> &amp; <font color="Maroon" title="c14">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c15">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X3</font> &amp; <font color="Maroon" title="c16">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X4</font> &amp; <font color="Maroon" title="c17">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X5</font> &amp; <font color="Maroon" title="c18">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X6</font> &amp; <font color="Maroon" title="c19">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X7</font> &amp; <font color="Maroon" title="c11">x1234567</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><font color="Maroon" title="c13">x1</font>,<font color="Maroon" title="c14">x2</font>,<font color="Maroon" title="c15">x3</font>,<font color="Maroon" title="c16">x4</font>,<font color="Maroon" title="c17">x5</font>,<font color="Maroon" title="c18">x6</font>,<font color="Maroon" title="c19">x7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span> )
 <b>by </b><i><a class="txt" href="#E4:107_1"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="mcart_3.html#T71" target="_self" title="MCART_3:th.71">MC371</a></i>;<br/><a NAME="E9:107_1"/>
<font color="Maroon" title="c10">y</font> <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"><font color="Maroon" title="c13">x1</font>,<font color="Maroon" title="c14">x2</font>,<font color="Maroon" title="c15">x3</font>,<font color="Maroon" title="c16">x4</font>,<font color="Maroon" title="c17">x5</font>,<font color="Maroon" title="c18">x6</font>,<font color="Maroon" title="c19">x7</font>,<font color="Maroon" title="c12">x8</font></span><a href="mcart_3.html#K18" title="MCART_3:func.18">]</a></span>
 <b>by </b><i><a class="txt" href="#E6:107_1"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="#E8:107_1"><i><font color="Green" title="E77">A6</font></i></a></i>;<br/><b>hence </b><a NAME="E10:107_1"/>
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Z</font>
 <b>by </b><i><a class="txt" href="#E1:107"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E5:107_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="#E8:107_1"><i><font color="Green" title="E77">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:107"/>
<font color="Maroon" title="c9">Z</font> <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"><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_3.html#K19" title="MCART_3:func.19">:]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</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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