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<div class="add">

<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">Z</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"> ( (  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="c10">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>, <font color="Olive" title="b10">x9</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="b10">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X9</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_2.html#K36" title="MCART_2:func.36">[</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>,<font color="Olive" title="b10">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> ) ) ) implies <font color="Maroon" title="c10">Z</font> <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="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> )</span><br/>



















<span class="kw">assume </span><a NAME="E1:171"/><span class="lab"><font color="Green" title="E113">A1</font></span>: 
 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="c10">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>, <font color="Olive" title="b10">x9</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="b10">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X9</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_2.html#K36" title="MCART_2:func.36">[</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>,<font color="Olive" title="b10">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">Z</font> <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="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></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="171_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">y</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"> ( ( <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font> implies <font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ) &amp; ( <font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font> ) )</span><br/><span class="kw">thus </span><a NAME="E1:171_1"/>
( <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font> implies <font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="171_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:171_1_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">x1</font>, <font color="Maroon" title="c13">x2</font>, <font color="Maroon" title="c14">x3</font>, <font color="Maroon" title="c15">x4</font>, <font color="Maroon" title="c16">x5</font>, <font color="Maroon" title="c17">x6</font>, <font color="Maroon" title="c18">x7</font>, <font color="Maroon" title="c19">x8</font>, <font color="Maroon" title="c20">x9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:171_1_1"/><span class="lab"><font color="Green" title="E114">A2</font></span>: 
( <font color="Maroon" title="c12">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="c13">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="c14">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="c15">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="c16">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="c17">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="c18">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="c19">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font> )
 <span class="kw">and </span><br/><a NAME="E4:171_1_1"/><span class="lab"><font color="Green" title="E115">A3</font></span>: 
( <font color="Maroon" title="c20">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X9</font> &amp; <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K36" title="MCART_2:func.36">[</a><span class="default"><font color="Maroon" title="c12">x1</font>,<font color="Maroon" title="c13">x2</font>,<font color="Maroon" title="c14">x3</font>,<font color="Maroon" title="c15">x4</font>,<font color="Maroon" title="c16">x5</font>,<font color="Maroon" title="c17">x6</font>,<font color="Maroon" title="c18">x7</font>,<font color="Maroon" title="c19">x8</font>,<font color="Maroon" title="c20">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:171"><span class="lab"><font color="Green" title="E113">A1</font></span></a></span>;<br/>
<a NAME="E5:171_1_1"/>
<span class="p1"><a href="mcart_2.html#K26" title="MCART_2:func.26">[</a><span class="default"><font color="Maroon" title="c12">x1</font>,<font color="Maroon" title="c13">x2</font>,<font color="Maroon" title="c14">x3</font>,<font color="Maroon" title="c15">x4</font>,<font color="Maroon" title="c16">x5</font>,<font color="Maroon" title="c17">x6</font>,<font color="Maroon" title="c18">x7</font>,<font color="Maroon" title="c19">x8</font></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:171_1_1"><span class="lab"><font color="Green" title="E114">A2</font></span></a>, <a class="ref" href="mcart_2.html#T151" target="_self" title="MCART_2:th.151">Th153</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:171_1_1"/>
<font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:171_1_1"><span class="lab"><font color="Green" title="E115">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</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/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:171_1"/>
<font color="Maroon" title="c11">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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>,<font color="Maroon" title="c9">X9</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">x12345678</font>, <font color="Maroon" title="c13">x9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:171_1"/><span class="lab"><font color="Green" title="E114">A4</font></span>: 
<font color="Maroon" title="c12">x12345678</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E5:171_1"/><span class="lab"><font color="Green" title="E115">A5</font></span>: 
<font color="Maroon" title="c13">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X9</font>
 <span class="kw">and </span><br/><a NAME="E6:171_1"/><span class="lab"><font color="Green" title="E116">A6</font></span>: 
<font color="Maroon" title="c11">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="c12">x12345678</font>,<font color="Maroon" title="c13">x9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c14">x1</font>, <font color="Maroon" title="c15">x2</font>, <font color="Maroon" title="c16">x3</font>, <font color="Maroon" title="c17">x4</font>, <font color="Maroon" title="c18">x5</font>, <font color="Maroon" title="c19">x6</font>, <font color="Maroon" title="c20">x7</font>, <font color="Maroon" title="c21">x8</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:171_1"/><span class="lab"><font color="Green" title="E117">A7</font></span>: 
( <font color="Maroon" title="c14">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="c15">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="c16">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="c17">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="c18">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="c19">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="c20">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="c21">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X8</font> )
 <span class="kw">and </span><br/><a NAME="E9:171_1"/><span class="lab"><font color="Green" title="E118">A8</font></span>: 
<font color="Maroon" title="c12">x12345678</font> <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"><font color="Maroon" title="c14">x1</font>,<font color="Maroon" title="c15">x2</font>,<font color="Maroon" title="c16">x3</font>,<font color="Maroon" title="c17">x4</font>,<font color="Maroon" title="c18">x5</font>,<font color="Maroon" title="c19">x6</font>,<font color="Maroon" title="c20">x7</font>,<font color="Maroon" title="c21">x8</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="txt" href="#E4:171_1"><span class="lab"><font color="Green" title="E114">A4</font></span></a>, <a class="ref" href="mcart_2.html#T150" target="_self" title="MCART_2:th.150">Th152</a></span>;<br/><a NAME="E10:171_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K36" title="MCART_2:func.36">[</a><span class="default"><font color="Maroon" title="c14">x1</font>,<font color="Maroon" title="c15">x2</font>,<font color="Maroon" title="c16">x3</font>,<font color="Maroon" title="c17">x4</font>,<font color="Maroon" title="c18">x5</font>,<font color="Maroon" title="c19">x6</font>,<font color="Maroon" title="c20">x7</font>,<font color="Maroon" title="c21">x8</font>,<font color="Maroon" title="c13">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:171_1"><span class="lab"><font color="Green" title="E116">A6</font></span></a>, <a class="txt" href="#E9:171_1"><span class="lab"><font color="Green" title="E118">A8</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E11:171_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:171"><span class="lab"><font color="Green" title="E113">A1</font></span></a>, <a class="txt" href="#E5:171_1"><span class="lab"><font color="Green" title="E115">A5</font></span></a>, <a class="txt" href="#E8:171_1"><span class="lab"><font color="Green" title="E117">A7</font></span></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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:171"/>
<font color="Maroon" title="c10">Z</font> <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="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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T1" title="TARSKI:th.1">TARSKI:1</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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