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<b>let </b><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> ;<br/>

<b>assume </b><a NAME="E1:6"/>
<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="borsuk_5.html#R2" title="BORSUK_5:pred.2">are_mutually_different</a> 
 ;<br/>

<a NAME="E2:6"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
( <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> &amp; <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="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="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</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="c7">x7</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> &amp; <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="c2">x2</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="c6">x6</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="c7">x7</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> &amp; <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="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</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="c7">x7</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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> )
 
<b>by </b><i><a class="ref" href="borsuk_5.html#D2" target="_self" title="BORSUK_5:def.2">Def2</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
<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="borsuk_5.html#R1" title="BORSUK_5:pred.1">are_mutually_different</a> 
 
<b>by </b><i><a class="ref" href="borsuk_5.html#D1" target="_self" title="BORSUK_5:def.1">Def1</a></i>;<br/>
<a NAME="E4:6"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">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
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T4" target="_self" title="BORSUK_5:th.4">Th4</a></i>;<br/>
<a NAME="E5:6"/>
( 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> &amp; <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> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <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> )
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="enumset1.html#T61" title="ENUMSET1:th.61">ENUMSET1:61</a></i>;<br/>
<b>hence </b> <a href="card_1.html#K4" title="CARD_1:func.4">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
<b>by </b><i><a class="txt" href="borsuk_5.html#E4:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="card_2.html#T54" title="CARD_2:th.54">CARD_2:54</a></i>
<br/>.= 
7

;<br/><br/>


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