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<span class="kw">let </span><font color="Maroon" title="c1">y2</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> 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"> 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_2.html#K27" title="MCART_2:func.27">[:</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></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</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; ( 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>  st <font color="Olive" title="b1">x</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="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></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> holds <br/><font color="Maroon" title="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">xx2</font> ) holds <br/><font color="Maroon" title="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K29" title="MCART_2:func.29">`2</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c10">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span>; <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="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; ( 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>  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#K26" title="MCART_2:func.26">[</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></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> holds <br/><font color="Maroon" title="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">xx2</font> ) implies <font color="Maroon" title="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K29" title="MCART_2:func.29">`2</a>  )</span><br/>



















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:130"/><span class="lab"><font color="Green" title="E92">A1</font></span>: 
( <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>  )
 <span class="kw">and </span><br/><a NAME="E2:130"/><span class="lab"><font color="Green" title="E93">A2</font></span>: 
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>  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#K26" title="MCART_2:func.26">[</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></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> holds <br/><font color="Maroon" title="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">xx2</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="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K29" title="MCART_2:func.29">`2</a> </span><br/>

<a NAME="E3:130"/>
<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#K26" title="MCART_2:func.26">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K28" title="MCART_2:func.28">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K29" title="MCART_2:func.29">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K30" title="MCART_2:func.30">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K31" title="MCART_2:func.31">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K32" title="MCART_2:func.32">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K33" title="MCART_2:func.33">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K34" title="MCART_2:func.34">`7</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K35" title="MCART_2:func.35">`8</a> </span>)</span></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="#E1:130"><span class="lab"><font color="Green" title="E92">A1</font></span></a>, <a class="ref" href="mcart_2.html#T138" target="_self" title="MCART_2:th.138">Th138</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:130"/>
<font color="Maroon" title="c1">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x</font> <a href="mcart_2.html#K29" title="MCART_2:func.29">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130"><span class="lab"><font color="Green" title="E93">A2</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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