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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>, <font color="Maroon" title="c7">x7</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>,<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>,<font color="Maroon" title="c7">x7</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">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#K5" title="ENUMSET1:func.5">{</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>,<font color="Maroon" title="c7">x7</font></span><a href="enumset1.html#K5" title="ENUMSET1:func.5">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 )</span><br/>

<a NAME="E1:6"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<span class="p1"><a href="enumset1.html#K5" title="ENUMSET1:func.5">{</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>,<font color="Maroon" title="c7">x7</font></span><a href="enumset1.html#K5" title="ENUMSET1:func.5">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="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="c7">x7</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#T61" title="ENUMSET1:th.61">ENUMSET1:61</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:6"/><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>,<font color="Maroon" title="c7">x7</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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#K5" title="ENUMSET1:func.5">{</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>,<font color="Maroon" title="c7">x7</font></span><a href="enumset1.html#K5" title="ENUMSET1:func.5">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7</span><br/>

<a NAME="E3:6"/><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#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E4:6"/><span class="lab"><font color="Green" title="E6">A4</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="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E5:6"/><span class="lab"><font color="Green" title="E7">A5</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="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E6:6"/><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="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E7:6"/><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="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E8:6"/><span class="lab"><font color="Green" title="E10">A8</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E9:6"/><span class="lab"><font color="Green" title="E11">A9</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E10:6"/><span class="lab"><font color="Green" title="E12">A10</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E11:6"/><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="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E12:6"/><span class="lab"><font color="Green" title="E14">A12</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E13:6"/><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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E14:6"/><span class="lab"><font color="Green" title="E16">A14</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E15:6"/><span class="lab"><font color="Green" title="E17">A15</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E16:6"/><span class="lab"><font color="Green" title="E18">A16</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E17:6"/><span class="lab"><font color="Green" title="E19">A17</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E18:6"/><span class="lab"><font color="Green" title="E20">A18</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E19:6"/><span class="lab"><font color="Green" title="E21">A19</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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E20:6"/><span class="lab"><font color="Green" title="E22">A20</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="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E21:6"/>
<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="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E22:6"/><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>,<font color="Maroon" title="c6">x6</font> <a href="zfmisc_1.html#R4" title="ZFMISC_1:pred.4">are_mutually_different</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E12:6"><span class="lab"><font color="Green" title="E14">A12</font></span></a>, <a class="txt" href="#E11:6"><span class="lab"><font color="Green" title="E13">A11</font></span></a>, <a class="txt" href="#E20:6"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E19:6"><span class="lab"><font color="Green" title="E21">A19</font></span></a>, <a class="txt" href="#E18:6"><span class="lab"><font color="Green" title="E20">A18</font></span></a>, <a class="txt" href="#E17:6"><span class="lab"><font color="Green" title="E19">A17</font></span></a>, <a class="txt" href="#E16:6"><span class="lab"><font color="Green" title="E18">A16</font></span></a>, <a class="txt" href="#E15:6"><span class="lab"><font color="Green" title="E17">A15</font></span></a>, <a class="txt" href="#E14:6"><span class="lab"><font color="Green" title="E16">A14</font></span></a>, <a class="txt" href="#E13:6"><span class="lab"><font color="Green" title="E15">A13</font></span></a>, <a class="txt" href="#E9:6"><span class="lab"><font color="Green" title="E11">A9</font></span></a>, <a class="txt" href="#E8:6"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="txt" href="#E10:6"><span class="lab"><font color="Green" title="E12">A10</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="E23:6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A21</font></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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_5.html#T4" target="_self" title="BORSUK_5:th.4">Th4</a></span>;<br/>
<a NAME="E24:6"/><span class="lab"><font color="Green" title="E24">A22</font></span>: 
<font color="Maroon" title="c6">x6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E25:6"/>
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E26:6"/><span class="kw">then </span>
not <font color="Maroon" title="c7">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="txt" href="#E6:6"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E24:6"><span class="lab"><font color="Green" title="E24">A22</font></span></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</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#K5" title="ENUMSET1:func.5">{</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>,<font color="Maroon" title="c7">x7</font></span><a href="enumset1.html#K5" title="ENUMSET1:func.5">}</a></span> = 
6 <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="#E23:6"><span class="lab"><font color="Green" title="E23">A21</font></span></a>, <a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="card_2.html#T54" title="CARD_2:th.54">CARD_2:54</a></span>
<br/>.= 
7

;<br/> <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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