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<b>take </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/>

<b>thus </b><a NAME="E1:2_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:2_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#R2">meets</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:2_1_1_1"/><i><font color="Green">E2</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="freealg.html#E3:2_1_1_1"><i><font color="Green">E2</font></i></a></i>;<br/><a NAME="E5:2_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="freealg.html#E3:2_1_1_1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="nat_1.html#T18">NAT_1:18</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:2_1_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:2_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="freealg.html#V1" target="_self">missing_with_Nat</a>
 <b>by </b><i><a class="ref" href="freealg.html#D1" target="_self">Def1</a></i>;<br/>


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