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<span class="kw">let </span><font color="Maroon" title="c1">y3</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> 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">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#K2" title="MCART_2:func.2">[:</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></span><a href="mcart_2.html#K2" title="MCART_2:func.2">:]</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; (  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>  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#K1" title="MCART_2:func.1">[</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></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span> holds <br/><font color="Maroon" title="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">xx3</font> ) holds <br/><font color="Maroon" title="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K5" title="MCART_2:func.5">`3</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c7">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#K2" title="MCART_2:func.2">[:</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></span><a href="mcart_2.html#K2" title="MCART_2: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="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; (  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>  st <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</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></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span> holds <br/><font color="Maroon" title="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">xx3</font> ) implies <font color="Maroon" title="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K5" title="MCART_2:func.5">`3</a>  )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:29"/><span class="lab"><font color="Green" title="E23">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>  )
 <span class="kw">and </span><br/><a NAME="E2:29"/><span class="lab"><font color="Green" title="E24">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>  st <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</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></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span> holds <br/><font color="Maroon" title="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">xx3</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="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K5" title="MCART_2:func.5">`3</a> </span><br/>

<a NAME="E3:29"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K3" title="MCART_2:func.3">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K4" title="MCART_2:func.4">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K5" title="MCART_2:func.5">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K6" title="MCART_2:func.6">`4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K7" title="MCART_2:func.7">`5</a></span>)</span></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="mcart_2.html#T17" target="_self" title="MCART_2:th.17">Th19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:29"/>
<font color="Maroon" title="c1">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K5" title="MCART_2:func.5">`3</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E24">A2</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/>


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