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<b>let </b><font color="Maroon">x</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/>

<b>assume </b><a NAME="E1:131"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,2,3,4</span><a href="enumset1.html#K3">}</a></span>
 ;<br/>

<a NAME="E2:131"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">2,3,4</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T48">ENUMSET1:48</a></i>;<br/>
<a NAME="E3:131"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">2,3,4</span><a href="enumset1.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:131"/><b>then </b><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 4 )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:131"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K1">VAR</a> 
 
;<br/>
<a NAME="E6:131"/><b>then </b>
 ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">i</font> &amp; 5 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> )
 
;<br/>
<b>hence </b><a NAME="E7:131"/>
contradiction
 <b>by </b><i><a class="ref" href="zf_lang1.html#T6" target="_self">Th6</a></i>;<br/>


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