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<span class="kw">let </span><font color="Maroon" title="c11">y</font>, <font color="Maroon" title="c12">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">X8</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c10">x</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="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> holds <br/><font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">x8</font> ) &amp; ( for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c10">x</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="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> holds <br/><font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">x8</font> ) implies <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:157_8_2"/><span class="lab"><font color="Green" title="E103">A31</font></span>: 
for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c10">x</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="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> holds <br/><font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">x8</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c10">x</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="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> &amp; not <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">x8</font> ) or <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:157_8_2"/><span class="lab"><font color="Green" title="E104">A32</font></span>: 
for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c10">x</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="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_2.html#K36" title="MCART_2:func.36">]</a></span> holds <br/><font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">x8</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c13">xx1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c14">xx2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c15">xx3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X3</font>, <font color="Maroon" title="c16">xx4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font>, <font color="Maroon" title="c17">xx5</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font>, <font color="Maroon" title="c18">xx6</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X6</font>, <font color="Maroon" title="c19">xx7</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">X7</font>, <font color="Maroon" title="c20">xx8</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">X8</font>, <font color="Maroon" title="c21">xx9</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">X9</font><span class="kw"> such that </span><br/><a NAME="E4:157_8_2"/><span class="lab"><font color="Green" title="E105">A33</font></span>: 
<font color="Maroon" title="c10">x</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="c13">xx1</font>,<font color="Maroon" title="c14">xx2</font>,<font color="Maroon" title="c15">xx3</font>,<font color="Maroon" title="c16">xx4</font>,<font color="Maroon" title="c17">xx5</font>,<font color="Maroon" title="c18">xx6</font>,<font color="Maroon" title="c19">xx7</font>,<font color="Maroon" title="c20">xx8</font>,<font color="Maroon" title="c21">xx9</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="#E1:157"><span class="lab"><font color="Green" title="E102">A1</font></span></a>, <a class="ref" href="mcart_2.html#T180" target="_self" title="MCART_2:th.180">Th180</a></span>;<br/>
<a NAME="E5:157_8_2"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">xx8</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:157_8_2"><span class="lab"><font color="Green" title="E105">A33</font></span></a>, <a class="txt" href="#E1:157_8_2"><span class="lab"><font color="Green" title="E103">A31</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:157_8_2"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:157_8_2"><span class="lab"><font color="Green" title="E105">A33</font></span></a>, <a class="txt" href="#E2:157_8_2"><span class="lab"><font color="Green" title="E104">A32</font></span></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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