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<b>let </b><font color="Maroon" title="c1">y4</font>, <font color="Maroon" title="c2">X1</font>, <font color="Maroon" title="c3">X2</font>, <font color="Maroon" title="c4">X3</font>, <font color="Maroon" title="c5">X4</font>, <font color="Maroon" title="c6">X5</font>, <font color="Maroon" title="c7">X6</font>, <font color="Maroon" title="c8">X7</font>, <font color="Maroon" title="c9">X8</font>, <font color="Maroon" title="c10">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"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c4">X3</font>,<font color="Maroon" title="c5">X4</font>,<font color="Maroon" title="c6">X5</font>,<font color="Maroon" title="c7">X6</font>,<font color="Maroon" title="c8">X7</font>,<font color="Maroon" title="c9">X8</font>,<font color="Maroon" title="c10">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span>  st <font color="Maroon" title="c2">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c9">X8</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">X9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; ( for <font color="Olive" title="b2">xx1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X1</font><br/> for <font color="Olive" title="b3">xx2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X2</font><br/> for <font color="Olive" title="b4">xx3</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X3</font><br/> for <font color="Olive" title="b5">xx4</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X4</font><br/> for <font color="Olive" title="b6">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X5</font><br/> for <font color="Olive" title="b7">xx6</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">X6</font><br/> for <font color="Olive" title="b8">xx7</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">X7</font><br/> for <font color="Olive" title="b9">xx8</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">X8</font><br/> for <font color="Olive" title="b10">xx9</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c10">X9</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><font color="Olive" title="b2">xx1</font>,<font color="Olive" title="b3">xx2</font>,<font color="Olive" title="b4">xx3</font>,<font color="Olive" title="b5">xx4</font>,<font color="Olive" title="b6">xx5</font>,<font color="Olive" title="b7">xx6</font>,<font color="Olive" title="b8">xx7</font>,<font color="Olive" title="b9">xx8</font>,<font color="Olive" title="b10">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span> holds <br/><font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">xx4</font> ) holds <br/><font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span><br/><b>let </b><font color="Maroon" title="c11">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c4">X3</font>,<font color="Maroon" title="c5">X4</font>,<font color="Maroon" title="c6">X5</font>,<font color="Maroon" title="c7">X6</font>,<font color="Maroon" title="c8">X7</font>,<font color="Maroon" title="c9">X8</font>,<font color="Maroon" title="c10">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</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="c2">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c9">X8</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">X9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; ( for <font color="Olive" title="b1">xx1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X1</font><br/> for <font color="Olive" title="b2">xx2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X2</font><br/> for <font color="Olive" title="b3">xx3</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X3</font><br/> for <font color="Olive" title="b4">xx4</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X4</font><br/> for <font color="Olive" title="b5">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X5</font><br/> for <font color="Olive" title="b6">xx6</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">X6</font><br/> for <font color="Olive" title="b7">xx7</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">X7</font><br/> for <font color="Olive" title="b8">xx8</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">X8</font><br/> for <font color="Olive" title="b9">xx9</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c10">X9</font>  st <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><font color="Olive" title="b1">xx1</font>,<font color="Olive" title="b2">xx2</font>,<font color="Olive" title="b3">xx3</font>,<font color="Olive" title="b4">xx4</font>,<font color="Olive" title="b5">xx5</font>,<font color="Olive" title="b6">xx6</font>,<font color="Olive" title="b7">xx7</font>,<font color="Olive" title="b8">xx8</font>,<font color="Olive" title="b9">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span> holds <br/><font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">xx4</font> ) implies <font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a>  )</span><br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:135"/><i><font color="Green" title="E92">A1</font></i>: 
( <font color="Maroon" title="c2">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c9">X8</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c10">X9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>and </b><br/><a NAME="E2:135"/><i><font color="Green" title="E93">A2</font></i>: 
for <font color="Olive" title="b1">xx1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X1</font><br/> for <font color="Olive" title="b2">xx2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X2</font><br/> for <font color="Olive" title="b3">xx3</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X3</font><br/> for <font color="Olive" title="b4">xx4</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X4</font><br/> for <font color="Olive" title="b5">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X5</font><br/> for <font color="Olive" title="b6">xx6</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">X6</font><br/> for <font color="Olive" title="b7">xx7</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">X7</font><br/> for <font color="Olive" title="b8">xx8</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">X8</font><br/> for <font color="Olive" title="b9">xx9</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c10">X9</font>  st <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><font color="Olive" title="b1">xx1</font>,<font color="Olive" title="b2">xx2</font>,<font color="Olive" title="b3">xx3</font>,<font color="Olive" title="b4">xx4</font>,<font color="Olive" title="b5">xx5</font>,<font color="Olive" title="b6">xx6</font>,<font color="Olive" title="b7">xx7</font>,<font color="Olive" title="b8">xx8</font>,<font color="Olive" title="b9">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span> holds <br/><font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">xx4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span><br/>

<a NAME="E3:135"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K34" title="MCART_3:func.34">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K35" title="MCART_3:func.35">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K36" title="MCART_3:func.36">`7</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K37" title="MCART_3:func.37">`8</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K38" title="MCART_3:func.38">`9</a> </span>)</span></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
 
<b>by </b><i><a class="txt" href="#E1:135"><i><font color="Green" title="E92">A1</font></i></a>, <a class="ref" href="mcart_3.html#T144" target="_self" title="MCART_3:th.144">Th67</a></i>;<br/>
<b>hence </b><a NAME="E4:135"/>
<font color="Maroon" title="c1">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> 
 <b>by </b><i><a class="txt" href="#E2:135"><i><font color="Green" title="E93">A2</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/>


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