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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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_different</a>  implies  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</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="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 )</span><br/>









<a NAME="E1:63"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
<span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</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="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1: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></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">x5</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T10" title="ENUMSET1:th.10">ENUMSET1:10</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:63"/><span class="lab"><font color="Green" title="E46">A2</font></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> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_different</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</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="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5</span><br/>

<a NAME="E3:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A3</font></span>: 
( <font color="Maroon" title="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font> &amp; <font color="Maroon" title="c4">x4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D7" title="ZFMISC_1:def.7">ZFMISC_1:def 7</a></span>;<br/>
<a NAME="E4:63"/><span class="lab"><font color="Green" title="E48">A4</font></span>: 
( <font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x4</font> &amp; <font color="Maroon" title="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x4</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D7" title="ZFMISC_1:def.7">ZFMISC_1:def 7</a></span>;<br/>
<a NAME="E5:63"/><span class="lab"><font color="Green" title="E49">A5</font></span>: 
( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x4</font> &amp; <font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">x3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D7" title="ZFMISC_1:def.7">ZFMISC_1:def 7</a></span>;<br/>
<a NAME="E6:63"/>
( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font> &amp; <font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D7" title="ZFMISC_1:def.7">ZFMISC_1:def 7</a></span>;<br/>
<a NAME="E7:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A6</font></span>: 
 not <font color="Maroon" title="c5">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1: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></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></span>;<br/>
<a NAME="E8:63"/>
( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x2</font> &amp; <font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">x3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D7" title="ZFMISC_1:def.7">ZFMISC_1:def 7</a></span>;<br/>
<a NAME="E9:63"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1: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></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="ref" href="card_2.html#T59" target="_self" title="CARD_2:th.59">Th78</a></span>;<br/>
<span class="kw">hence </span> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</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="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> = 
4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:63"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="card_2.html#T41" target="_self" title="CARD_2:th.41">Th54</a></span>
<br/>.= 
5

;<br/> <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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