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<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> 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"> ( <font color="Maroon" title="c1">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="c2">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="c3">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="c4">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="c5">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>  implies 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="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></span><a href="mcart_2.html#K2" title="MCART_2:func.2">:]</a></span>  ex <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="c1">X1</font> ex <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="c2">X2</font> ex <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="c3">X3</font> ex <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="c4">X4</font> ex <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="c5">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> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
( <font color="Maroon" title="c1">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="c2">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="c3">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="c4">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>  )
 <span class="kw">and </span><br/><a NAME="E2:22"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c5">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> 
 ; <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#K2" title="MCART_2:func.2">[:</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></span><a href="mcart_2.html#K2" title="MCART_2:func.2">:]</a></span>  ex <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="c1">X1</font> ex <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="c2">X2</font> ex <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="c3">X3</font> ex <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="c4">X4</font> ex <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="c5">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></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">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="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></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="Red">::  thesis: </font></span></a><span class="hide">  ex <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="c1">X1</font> ex <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="c2">X2</font> ex <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="c3">X3</font> ex <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="c4">X4</font> ex <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="c5">X5</font> st <font color="Maroon" title="c6">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></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">x9</font> = <font color="Maroon" title="c6">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</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></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>,<font color="Maroon" title="c5">X5</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ;<br/>
<a NAME="E4:22"/>
<span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</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></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <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">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="mcart_1.html#T55" title="MCART_1:th.55">MCART_1:55</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">x1234</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</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></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>, <font color="Maroon" title="c9">xx5</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font><span class="kw"> such that </span><br/><a NAME="E6:22"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c7">x9</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="c8">x1234</font>,<font color="Maroon" title="c9">xx5</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="mcart_2.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">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="c11">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="c12">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="c13">xx4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font><span class="kw"> such that </span><br/><a NAME="E8:22"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c8">x1234</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">xx1</font>,<font color="Maroon" title="c11">xx2</font>,<font color="Maroon" title="c12">xx3</font>,<font color="Maroon" title="c13">xx4</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="mcart_2.html#E3"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">xx1</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">xx2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font> ex <font color="Olive" title="b2">xx3</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X3</font> ex <font color="Olive" title="b3">xx4</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font> ex <font color="Olive" title="b4">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font> st <font color="Maroon" title="c6">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="Maroon" title="c10">xx1</font>,<font color="Olive" title="b1">xx2</font>,<font color="Olive" title="b2">xx3</font>,<font color="Olive" title="b3">xx4</font>,<font color="Olive" title="b4">xx5</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c11">xx2</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">xx3</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X3</font> ex <font color="Olive" title="b2">xx4</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font> ex <font color="Olive" title="b3">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font> st <font color="Maroon" title="c6">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="Maroon" title="c10">xx1</font>,<font color="Maroon" title="c11">xx2</font>,<font color="Olive" title="b1">xx3</font>,<font color="Olive" title="b2">xx4</font>,<font color="Olive" title="b3">xx5</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c12">xx3</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">xx4</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font> ex <font color="Olive" title="b2">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font> st <font color="Maroon" title="c6">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="Maroon" title="c10">xx1</font>,<font color="Maroon" title="c11">xx2</font>,<font color="Maroon" title="c12">xx3</font>,<font color="Olive" title="b1">xx4</font>,<font color="Olive" title="b2">xx5</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c13">xx4</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">xx5</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font> st <font color="Maroon" title="c6">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="Maroon" title="c10">xx1</font>,<font color="Maroon" title="c11">xx2</font>,<font color="Maroon" title="c12">xx3</font>,<font color="Maroon" title="c13">xx4</font>,<font color="Olive" title="b1">xx5</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c9">xx5</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="c6">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="Maroon" title="c10">xx1</font>,<font color="Maroon" title="c11">xx2</font>,<font color="Maroon" title="c12">xx3</font>,<font color="Maroon" title="c13">xx4</font>,<font color="Maroon" title="c9">xx5</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span></span><br/>

<span class="kw">thus </span><a NAME="E9:22"/>
<font color="Maroon" title="c6">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="Maroon" title="c10">xx1</font>,<font color="Maroon" title="c11">xx2</font>,<font color="Maroon" title="c12">xx3</font>,<font color="Maroon" title="c13">xx4</font>,<font color="Maroon" title="c9">xx5</font></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="#E6:22"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E17">A4</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/>


</div>
