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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>, <font color="Maroon" title="c6">x6</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>,<font color="Maroon" title="c6">x6</font> <a href="zfmisc_1.html#R4" title="ZFMISC_1:pred.4">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#K4" title="ENUMSET1: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>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c6">x6</font></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 )</span><br/>

<a NAME="E1:4"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<span class="p1"><a href="enumset1.html#K4" title="ENUMSET1: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>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c6">x6</font></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="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="c6">x6</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#T15" title="ENUMSET1:th.15">ENUMSET1:15</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:4"/><span class="lab"><font color="Green" title="E4">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>,<font color="Maroon" title="c6">x6</font> <a href="zfmisc_1.html#R4" title="ZFMISC_1:pred.4">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#K4" title="ENUMSET1: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>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c6">x6</font></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6</span><br/>

<a NAME="E3:4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A3</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="c3">x3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E4:4"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
<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="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E5:4"/><span class="lab"><font color="Green" title="E7">A5</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E6:4"/><span class="lab"><font color="Green" title="E8">A6</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="c4">x4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E7:4"/><span class="lab"><font color="Green" title="E9">A7</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="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E8:4"/><span class="lab"><font color="Green" title="E10">A8</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E9:4"/><span class="lab"><font color="Green" title="E11">A9</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="c3">x3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E10:4"/><span class="lab"><font color="Green" title="E12">A10</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="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E11:4"/><span class="lab"><font color="Green" title="E13">A11</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E12:4"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E13:4"/><span class="kw">then </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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E11:4"><span class="lab"><font color="Green" title="E13">A11</font></span></a>, <a class="txt" href="#E10:4"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="txt" href="#E9:4"><span class="lab"><font color="Green" title="E11">A9</font></span></a>, <a class="txt" href="#E8:4"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="txt" href="#E6:4"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="txt" href="#E5:4"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E6">A4</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="E14:4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A12</font></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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T63" title="CARD_2:th.63">CARD_2:63</a></span>;<br/>
<a NAME="E15:4"/><span class="lab"><font color="Green" title="E15">A13</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="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E16:4"/><span class="lab"><font color="Green" title="E16">A14</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="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E17:4"/><span class="lab"><font color="Green" title="E17">A15</font></span>: 
<font color="Maroon" title="c5">x5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E18:4"/><span class="lab"><font color="Green" title="E18">A16</font></span>: 
<font color="Maroon" title="c4">x4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E19:4"/>
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D8" title="ZFMISC_1:def.8">ZFMISC_1:def 8</a></span>;<br/>
<a NAME="E20:4"/><span class="kw">then </span>
 not <font color="Maroon" title="c6">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:4"><span class="lab"><font color="Green" title="E16">A14</font></span></a>, <a class="txt" href="#E15:4"><span class="lab"><font color="Green" title="E15">A13</font></span></a>, <a class="txt" href="#E18:4"><span class="lab"><font color="Green" title="E18">A16</font></span></a>, <a class="txt" href="#E17:4"><span class="lab"><font color="Green" title="E17">A15</font></span></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</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#K4" title="ENUMSET1: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>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c6">x6</font></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span> = 
5 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:4"><span class="lab"><font color="Green" title="E14">A12</font></span></a>, <a class="txt" href="#E1:4"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="card_2.html#T41" title="CARD_2:th.41">CARD_2:41</a></span>
<br/>.= 
6

;<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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